PHYS 241 Test 1
The figure above shows a section through two long thin concentric cylinders of radii a = 4.2 cm and b = 9.5 cm. The cylinders have equal and opposite charges per unit length, = 0.008 C/m. Find the magnitude of E (a) for r = 1.3 cm. and (b) for r = 6.6 cm.
(a) 0 N/C; (b) 2.17 109 N/C
Four capacitors are connected to a battery in the manner shown below. All capacitances are given in the table next to the figure, but the voltage V delivered by the battery is unknown. What is known is that, when connected to the network, the capacitor C1 acquires a charge of magnitude |Q1| = 15 nC = 15 10-9 C on each of its plates. (a) How much energy is stored in the capacitor C1 when the network is connected? (b) What is the voltage V supplied by the battery? (c) What is the charge Q4 on capacitor C4? (d) Until now, the gaps between the capacitor plates have been filled with vacuum. If the gaps between the plates of all four capacitors are now filled with a dielectric material with dielectric constant k > 1, the voltage drop across capacitor C1 will
(a) 1.41 x 10^-5 J (b) V = 5.88 kV (c) Q4 = 7.5 nC (d) Stay the same.
In the figure, three identical conducting spheres, A, B, and C form an equilateral triangle of side length d = 2.9 cm and have charges of -3Q, -6Q, and +12Q, respectively. (a) What is the magnitude of the electrostatic force (in Newtons) on sphere a from sphere C, if Q = 7.6 10-6 C? (b) In the figure above, the following steps are then taken: A and B are connected by a thin conducting wire and then disconnected; B is grounded by the wire and the wire is then removed; B and C are connected by the wire then disconnected. Now what is the magnitude of the electrostatic force (in Newtons) on sphere A from sphere C, if Q = 7.6 10 -6 C?
(a) 2.2 x 10^4 (b) 1.6 x 10^4
A solid spherical conductor of radius 15 cm has a charge Q = 6.5 nC on it. A second, initially uncharged, spherical conductor of radius 10 cm is moved toward the first until they touch and is then moved far away from it. (a) How much charge is there on the second sphere after the two spheres have been separated? (b) Calculate the common potential for either sphere.
(a) 2.6 nC (b) 234 V
At some instant the velocity components of an electron moving between two charged parallel plates are vx = 2.6 m/s and vy = 2.57 m/s. Suppose the electric field between the plates is given by E = 210j (N/C). (a) What is the magnitude of the acceleration (in m/s2 of the electron? immediately after the switch is moved to position A? (b) What is the direction of the acceleration of the electron? (c) What is the y-component of the velocity (in m/s) of the electron after its x coordinate has changed 4.2 cm?
(a) 3.69 x 10^13 (b) Perpendicular to the plates (c) -5.96 x 10^6
The figure below which shows the electric field lines of two point charges, A and B. Three positions are labeled 1, 2, and 3. (a) Which of the following is correct? (b) For three positions shown (1,2,3) in the figure, rank the magnitude of the electric field, from strongest to weakest.
(a) A is negative and larger in magnitude than B. (b) 1 > 2 > 3
An infinitely long, cylindrical conducting wire of radius a has a surface charge density (charge/unit area). (a) What is the magnitude of the electric field, E(r), outside the wire at a radial distance r from the wire's center? (b) Suppose > 0. If a positive charge is placed near the wire and released, it will move
(a) E(r) = (ó/E0)(a/r) (b) radially away from the central axis of the wire
Consider three flat infinite slabs of identical dimensions: their area A = 3 m2 is so large compared to their 2 cm thickness that they may be considered of infinite area for purposes of calculation. The figure below shows how they are positioned. Slabs a and b are made of glass (an excellent insulator), while the middle slab is made of copper (an excellent conductor). The copper slab is uncharged ( Qcopper = 0). However, the two glass slabs a and b are given total charges Qa = +2.5 nC and Qb = +7 nC, respectively, distributed uniformly throughout their volumes. (a) calculate the x-component of the electric field at the position x = -3.5 cm on the x-axis. (b) Calculate the total charge QR which resides on the right-hand face of the copper slab (i.e. at x = 0). (c) Calculate the electric potential difference (V(x=+3 cm) - V(x=-2 cm)) between the points x = +3 cm and x = -2 cm on the x axis.
(a) Ex = -84.7 N/C (b) QR = -2.25 nC (c) +2.54 V
In Figure A, a positive charge +Q is placed at the center of a cube. In Figure B, this same positive charge is moved upwards, closer to the upper surface of the cube. (a) Consider the total electric flux Fcube passing outward through the cube: (b) Consider the electric flux Fbottom passing outward through the shaded bottom face of the cube:
(a) Fcube is same for both figures. (b) Fbottom in Figure A > Fbottom in Figure B.
Two point charges are placed on the x-axis as shown. Let Q = 3 C and a = 5 m. (a) The y component of the electric field at point A is zero. (b) The magnitudes of the electric field at point A and point B are EA and EB, respectively. What is the ratio of EA over EB?
(a) True (b) Ea/Eb = 0.80
Consider two cylindrical, infinitely long charged rods with linear charge densities of ±? (where is non-zero) that lie perpendicular to the plane of the paper. Points A, B, C and D lie in a plane perpendicular to the charged rods. The locations of the points are indicated in the figure in terms of dimensions a and h. (The dashed lines form a rectangular grid.) (a) All points on the line between A and C have the same potential. (b) Which choice gives the correct relationship between the potential at points B, C, and D?
(a) True (b) VB > VC > VD
Three identical particles of mass m and charge q are assembled from infinity to form an equilateral triangle with sides of length d as shown in the figure. (a) Let W be the work required to assemble the triangle of charges by the following method. Charge A is first nailed down. Charge B is then moved from infinity and nailed down at a distance d from Charge A. Finally Charge C is moved in from infinity and nailed down at the apex of the triangle. The total work against the repulsive forces to assemble the triangle is: (b) After the triangle is assembled, the nail holding Charge C is removed and it flies off to infinity -- ultimately reaching a speed of vC. Charges A and B are still nailed down. Find vC.
(a) W = 3kq2/d (b) Vc = sqrt( 4kq^2/md)
As shown in the figure, a conducting spherical shell, of inner radius R and outer radius 2R, carries a total charge +2Q (Q > 0). A point charge +Q is placed at the center of the shell. Concentric to the conducting shell is an insulating spherical shell of radius 3R with negligible thickness. A charge +2Q is uniformly distributed on this insulating shell. (a) What is the magnitude of electric force on the charge at the center? (b) What is the total charge on the outer surface of the conducting shell? (c) What is the magnitude of the electric field at r = 0.5R?
(a) Zero (b) 3Q (c) kQ/ (.5R)^2
A solid sphere of radius a = 5 cm is centered at the origin. It is made of an insulating material and carries a uniform charge density with total charge Q1 = +10 C. It is surrounded by a hollow, concentric conducting shell of inner radius b = 15 cm and outer radius c = 20 cm. The outer shell has total charge Q = -5 C. (a) Compute the magnitude of the electric field at the point x = 30 cm on the x-axis. (b) What is the potential difference V(r) - V(0) for r < a (i.e., where r is inside the insulating sphere, and V(0) is the potential at the origin)? (c) The total charge on the outer surface of the conducting shell at r = c = 20 cm is
(a) |E| = 5 x 10^5 N/C (b) V(r) - V(0) = -kQ1r^2/ 2a^3 (c) Q2 + Q1
Figure below shows the electric field lines for a system of two point charges. (a) What are the relative magnitudes of the charges? (b) What are the signs of the charges?
(a) |q1| > |q2|; (b) q1 positive, q2 negative
The electric field lines (solid) and the equipotential lines (dashed) in a certain region of space are as shown below. (a) When a positive charge is moved from point A to point D, the work done by the electric field is (b) The electric field at C is
(a)equal to the work done by the field when the same charge is moved from point B to point C (b)equal to the electric field at B
10 C of charge are placed on a spherical conducting shell. A particle with a charge of -3 C is placed at the center of the cavity. The net charge on the inner surface of the shell is:
+3 C
A point charge -Q is at the center of a spherical conducting shell of inner radius R1 and outer radius R2 as shown in the figure below. What is the charge on the inner surface of the shell?
+Q
In the figure shown above, a plastic rod having a uniformly distributed charge -4.7 µC has been bent into a circular arc of radius 27 cm and central angle = 105 (degrees) (ignore the angle shown in the figure). With V = 0 at infinity, what is the electric potential at P, the center of curvature of the rod?
-1.56 x 10^5 V
How much work is required to set up the arrangement of the figure below if q = 2.27 pC, a = 70 cm, and the particles are initially infinitely far apart and at rest?
-1.71 x 10^-13 J
Three charges Q1 (= +8.0 C), Q2 (= -12.0 C), and Q3 (= +5.0 C) are arranged on the y-axis in the figure below. Q1 is located at (0,a), Q2 is located at the origin, and Q3 is located at (0,-a); a = 1.0 cm. Find the energy stored in the charge configuration of Q1, Q2, and Q3 (i.e., the work done that was necessary to assemble the three charges). A fourth charge q = +2 C is now brought in from infinity, and placed on the x-axis at a distance of d = 3 cm from the origin. Find the y-component of the net force of Q1, Q2, and Q3 on q.
-122 J, -17.1 N
Particles 1 and 2, with charges q1 and q2, respectively, are fixed in place, as shown in the figure below, but particle 3 is free to move. If the net electrostatic force on particle 3 due to particles 1 and 2 is zero and L23 = 1.3L12, what is the ratio q1/q2?
-3.13
In the figure above, three charged particles lie on a straight line and are separated by a distance d. Charges q1 and q2 are held fixed. Charge q3 is free to move but happens to be in equilibrium ( no electrostatic force acts on it ). If q2 = 1.05 C find the value of q1.
-4.2 microC
A charged particle is suspended at the center of two concentric spherical shells that are very thin and made of non-conducting material. Figure (a) shows across section. Figure (b) gives the net flux through a Gaussian sphere centered on the particle, as a function of the radius, r, of the sphere. (The vertical axis is marked in increments of 1 x 10^5 N · m2/C.) What is the net charge (in C) on shell A.
-5.31
In a certain situation, the electric potential varies along the x axis as shown in the graph shown below. For the interval ab determine the x component of the electric field, Ex .
-6.00 V/m
An isolated conductor of arbitrary shape has a net charge of +42.1 x10-6 C. Inside the conductor is a cavity within which is a point charge q = +7 x10-6 C. What is charge on the outer surface of the conductor?
-6.01 10-6 C
A charged oil drop with mass 2.5 10-4 kg is held in suspension by a downward electric field of 300 N/C. The charge (in Coulombs) on the drop is
-8.1 x 10^-6 C
A glass rod forms a quarter circle of radius R = 3.8 cm with a change of q = 2.1 10-11 C distributed uniformly along it. What is the x component of the electric field (in N/C) at the center of the arc (the origin of the axes shown)?
-83
A charge of 5.6 10-6 C is located in a uniform electric field of intensity 3.4 105 N/C. How much work (in Joules) is required to move this charge 51 cm along a path making an angle of 30?
.84
Points R and T are each a distance d from each of the two particles with charges of equal magnitude and opposite signs as shown. If = 1/(40), the work required to move a particle with a negative charge q from R to T is:
0
A thin spherical shell of radius 9.1 cm carries a uniform surface charge density of 8.4 10-9 C/m2. The magnitude of the electric field (in N/C) at r = 9 cm is approximately
0.00
How far apart must two protons be if the magnitude of the electrostatic force acting on either one is equal to 1.16 times one proton's weight at the Earth's surface ?
0.111 m
Two small spheres, each of mass m = 3 g and charge q are suspended from a point by threads of length L = 0.24 m. What is the charge on each sphere if the threads make an angle of = 15.8 with the vertical?
0.126 C
A particle of with a charge of 5 10-6 C and a mass of 20 grams moves uniformly with a speed of 6.5 m/s in a circular orbit around a stationary particle with a charge of -5 10-6 C. The radius of the orbit (in meters) is:
0.26
Four point charges q1 = 1 F, q2 = 2 F, q3 = 3 F, q4 = 4 F, are located in the corners of a square whose side s = 1 m. The electrostatic potential energy (in Joules) of this system of charges is:
0.286 J
A parallel plate capacitor of Area = 33 cm2 and separation distance d = 5 mm is charged by a battery of 60 V. If the air between the plates is replaced by a dielectric of dielectric constant = 2 with the battery still connected, then what is the ratio of the initial charge on the plates divided by the final charge on the plates?
0.5
A certain charge Q=2.05 C is divided into two parts, q and Q - q, which are separated by a certain distance. What must q be in terms of Q to maximize the electrostatic repulsion between the two charges?
0.50*Q
Which of the points in the electric field shown in the diagram are at the same potential?
1 and 4
Cube 1 and cube 2 are heavily charged plastic cubes that attract each other. Cube 3 is a conductor and is uncharged. Which of the following illustrates the forces between cubes 1 and 3, and between cubes 2 and 3?
1 down 2 down 3 up 3 up
The diagram shows four 1 F capacitors. The capacitance between points A and B is
1 microF
You have two flat metal plates, each of area 0.588 m2, with which to construct a parallel-plate capacitor. If the capacitance of the device is to be 4.32 F, what must be the separation between the plates?
1.2 10-6 m
A particle with charge q = -1.6 10-19C and a mass m = 10-27 kg, with an initial velocity vx = 107 m/s, travels in a uniform electric field Ex = 500 V/m. Determine the time (in seconds) it takes for the particle to come to rest.
1.25 x 10^-4 s
A spherical drop of mercury of radius R has a capacitance given by Cm= 4oR. If 3 such drops combine to form a single larger drop, what is its capacitance? (Give your answer in terms of Cm.)
1.44 Cm
Two small spheres, each of mass m = 3 g and charge q are suspended from a point by insulating threads of length L = 0.27 m. What is the charge (in Coulombs) on each sphere if the threads make an angle of = 17 with the vertical?
1.6 x 10^-7
You connect three capacitors as shown in the diagram. If the potential difference between A and B is 31.9 V, what is the total energy (in Joules) stored in this system of capacitors if C1 = 5.5 F, C2 = 4.5 F and C3 = 3 F?
11.74 x 10^-4 J
Find the magnitude of the electric field, E, in V/m at the point (1.7 m, -1.7 m) in the x-y plane for a the potential function V(x, y) = (x2y - y2x -10) V.
12.26
In the figure shown above, what value must R have if the current in the circuit is to be 3.3 mA? Take E1 = 3.1 V, E2 = 3.6 V, and r1 = r2 = 6.5 .
138.52 ohm
An oil droplet of mass 1.00 10-14 kg loses an electron while it is in an electric field of 1.00 10+6 N/C in a vacuum. The resulting change in acceleration (in m/s2) of the oil droplet is approximately
16
A square has equal positive charges at three of its corners, as shown below in the figure on the left. Which arrow in the figure on the right indicates the direction of the electric field at the point P?
2
The figure shows a graph of electric potential as a function of x. The scale of the verical is set by VS = 260 V. What is the magnitude of the x component of the force (in N) acting on a proton located at x = 0.2 m?
2.08 x 10^-16
What are the magnitude and direction of the electric field at the center of the square of Figure above if q= 1.88 x10-8 C and a= 4.77 cm ?
2.1 10^5 N/C, Vertical
Two charged concentric spheres have radii of 0.007 m and 0.017 m. The charge on the inner sphere is 3.5 10-8 C and that on the outer sphere is 1.5 10-8 C. Find the magnitude of the electric field (in N/C) at 0.012 m.
2.19 x 10^6
A uniform electric field of 300 N/C makes an angle of 23 with the dipole moment of an electric dipole. If the moment has a magnitude of 2.0 10-9 C · m, the torque exerted by the field has a magnitude of:
2.3 x 10^-7 N · m
An electric dipole p makes an angle of 30 with a uniform electric field of magnitude 340 N/C. If the torque on the dipole has a magnitude of 3.94 10-12 N · m, then calculate the magnitude of the dipole p.
2.32 x 10^-14 C · m
The Figure shows a rectangular array of charged particles fixed in place, with distance a = 35.5 cm and the charges show as integer multiples of q1 = 3.05 pC and q2 = 6.05 pC. With V = 0 at infinity, what is the net electric potential at the rectangle's center? (Hint: Thoughtful examination can reduce the calculation.)
2.45 Volts
A ring of radius 5.5 cm is in the yz plane with its center at the origin. The ring carries a uniform charge of 10.8 nC. A small particle of mass m = 10.7 g and charge of q = 5.4 nC is placed at x = 13.6 cm and released. The speed of the particle when it is a great distance from the ring is
2.59 cm/s
A solid spherical conductor has a radius of 18 cm. The electric field at 36 from the center of the sphere has a magnitude of 760 N/C. What is the charge density (in C/m2) on the sphere?
2.7 x 10^-8
A bob of mass m (m = 0.500 g), and charge magnitude Q (|Q| = 50.0 C) is held by a massless string in a uniform electric field E. If the bob makes an angle of 16.9 degrees with the vertical, what is the magnitude of the electric field E (N/C) and the sign of the bob charge Q?
29.8 and Q positive
A charge of 16 C is 10 cm above the center of a square of side length 20 cm. Find the flux through the square.
3.01 105 N m2/C
A non-conducting pipe has a uniform charge density of 58 C/m3. The inner radius of the pipe is 33 cm, while the outer radius is 39 cm. Calculate the magnitude of the electric field at r = 45 cm.
3.15 x 10^5 N/C
Refer to the Figure above. The battery has a potential difference of 14 volts and the capacitances C1, C2, and C3 are 3.3 F, 2.3 F, and 5.8 F, respectively. (Please remember that the values of all the other capacitors, besides C1, C2, and C3 are same as given in the figure.) What is the equivalent capacitance of all the capacitors and what is the charge stored on that equivalent capacitor?
3.24 microF; 45.35 microC
The figure below shows three flat plates, all of very large area. The two thin plates are made of insulating material and carry uniformly distributed surface charge densities of a = -3 C/m2 and b = 9 C/m2 respectively. The thick metal plate has a width w = 3.0 cm, and is initially uncharged (metal = 0). What is the magnitude of the electric field EA at the origin (the point marked A on the figure)? (Please use d1 = 4 cm, d2 = 12 cm.)
3.3 x 10^5 N/C
In the figure below, the resistances are R1 = 6 , R2 = 1 , R3 = 2 , R4 = 4 , R5 = 4 , R6 = 6 , and R7 = 8 . Find the equivalent resistance between points a and b.
3.57 ohm
An electron with a speed of 2.8 106 m/s moves into a uniform electric field of 500 N/C that is parallel to the electron's motion. How long does it take, in nanoseconds, for the electron to stop?
31
In the Figure, two curved plastic rods, one of charge +q and the other of charge -q, form a circle of radius R = 7.58 cm in the xy plane. The x-axis passes through both of the connecting points, and the charge is distributed uniformly on both rods. If q = 15.8 pC, what is the magnitude of the electric field produced at P, the center of the circle?
31.4 N/C
If you increase the charge on a parallel-plate capacitor from 4 C to 16 C and increase the plate separation from 1.8 mm to 3.6 mm, the energy stored in the capacitor changes by a factor of
32
Two identical conducting spheres A and B carry equal charge. They are separated by a distance much larger than their diameters. A third identical conducting sphere C is uncharged. Sphere C is first touched to A, then to B and finally removed. As a result, the electrostatic force between A and B, which was originally F, becomes:
3F/8
Three charges, +q, +2q, and +4q, are connected by strings as shown in the figure below (Assume that the middle charge is fixed in space and the other 2 charges are held there by the tension alone.): Find the tension T1.
3kq2/d2
Consider the following procedural steps to charge a metal sphere: 1. ground the sphere2. remove the ground from the sphere3. touch a charged rod to the sphere4. bring a charged rod near, but not touching, the sphere5. remove the charged rod To charge the sphere by induction, use the sequence
4, 1, 2, 5
In the figure shown above, what is the net potential at point P due to the four point charges, if q = 0.5 10-9 C, d = 2.8 m and V = 0 at infinity?
4.01 V
A uniformly charged sphere has a potential on its surface of 450 V. At a radial distance of 9.2 m from this surface, the potential is 150 V. What is the radius of the sphere? and what is the charge of the sphere?
4.6 m, 230 nC
The electric potential in a region of space is given by V(x,y) = (18 V)x + (39.6 V)y The magnitude (in V/m) and direction of the electric field are
43.5 V/m, 245 degrees
The figure below shows a parallel plate capacitor with plate area A = 10.4 cm2 and a plate separation 2d = 6.55 mm. The left half of the gap is filled with material of dielectric constant 1 = 20.4; the top of the right half is filled with material of dielectric constant 2 = 40.4; the bottom of the right half is filled with material of dielectric constant 3 = 55.5. What is the capacitance?
47.18 pF
Particle 1, with charge q1, and particle 2, with charge q2, are on the x-axis, with particl 1 at x = a and particle 2 at x = -2a. For the net force on a third charged particle, at the origin, to be zero, q1 and q2 must be related by q2 =
4q1
The distance between the K+ and Cl- ions in KCl is 2.80 10-10 m. Calculate the energy required to separate the two ions to an infinite distance apart, assuming them to be point charges initially at rest. Express your answer in eV.
5.14 eV
In a given lightning flash, the potential difference between a cloud and the ground is 2.47 109 V and the quantity of charge transferred is 21.1 C. What is the decrease in energy of the transferred charge? (Please give the magnitude.) If all that energy could be used to accelerate a 1154 kg automobile from rest, what would be the final speed of the automobile?
5.21 1010 J; 9.5 103 m/s
What equal positive charges would have to be placed on Earth and on the Moon to neutralize their gravitational attraction? (Mass of the Earth = 5.97e+24 kg, Mass of the Moon = 7.35e+22 kg, Average distance between Earth and the Moon = 3.85 108 m, G = 6.673e-11 N*m2/kg2)
5.7 x 10^13 C
An electric dipole, consisting of charges each of magnitude 2.89 nC and separated by 8.6 micrometers, is in an electric field of strength 1436 N/C. What is the magnitude of the difference in potential energy (in Joules) corresponding to dipole orientations parallel to and anti-parallel to the electric field?
7.14 x 10^-11
Five equal charges Q = 2.51 C each are equally spaced on a semicircle of radius R = 2.88 m as shown in the figure below: Find the magnitude of the force on a charge q = 1.12 C located at the center of the semicircle.
7.4 10-3 N
Calculate the electric dipole moment of an electron and a proton 4.79 mm apart.
7.66 10-22 C · m
Two charges (Q1 = -5.6 10-9 C, Q2 = -3.6 10-9 C) are a distance of 72 cm apart. How much work (in Joules) must be done to slowly move charges to a separation of 54 cm?
8.4 x 10^-8
A uniform electric field exists in a region between two oppositely charged plates. An electron is released from rest at the surface of the negatively charged plate and strikes the surface of the opposite plate, 2.2 cm away, in a time 1.7 10-7 s. What is the magnitude of the electric field?
8.669 N/C
A thin spherical shell of radius 9.1 cm carries a uniform surface charge density of 8.4 10-9 C/m2. The magnitude of the electric field (in N/C) at r = 9.3 cm is approximately
9.09 x 10^2
The voltage between the cathode and the screen of a television set is 26 kV. If we assume a speed of zero for an electron as it leaves the cathode, what is its speed (m/s) just before it hits the screen?
9.5 x 10^7
In a cathode-ray tube, an electron travels in a vacuum and enters a region between two deflection plates where there is an upward electric field of magnitude 2.7 105 N/C. If x1 = 16 cm and z1 = 1.9 cm, calculate the acceleration of the electron while it is between the deflection plates. Consider +x to the right, +y upwards, and +z coming out of page. (Neglect gravity.)
<0, -4.8 x 10^16, 0> m/s2
If you bring a positively charged insulator near two uncharged metallic spheres that are in contact and then separate the spheres while maintaining the position of the insulator, the sphere on the right will have
A positive charge
The electric potential is V(x,y) = Asin(kx)cos(ky), where A and k are constants. What is the y components of the electric field?
Asin(kx)sin(ky)
Charges +Q and -Q are arranged at the corners of a square as shown. When the electric field E and electric potential V are determined at P, the center of the square, we find that
E = 0 and V = 0
The figure below shows three flat plates, all of very large area. The two thin plates are made of insulating material and carry uniformly distributed surface charge densities of a = -3 C/m2 and b = 9 C/m2 respectively. The thick metal plate has a width w = 3.0 cm, and is initially uncharged (metal = 0). What is the sign of the surface charge densit LHS on the left-hand-side of the thick metal plate? (Please use d1 = 4 cm, d2 = 12 cm.)
LHS > 0
Positive charge Q is distributed uniformly throughout an insulating sphere of radius R, centered at the origin. A particle with charge Q is placed at x = 2R on the x axis. The magnitude of the electric field at x = R/2 on the x-axis is
Q/(72 Pi E0 R^2)
The diagram shows a particle with a charge Q1 = -Q and a particle with a charge Q2 = +Q. The electric field at a point P on the perpendicular bisector of the line joining them is
Upward arrow
The diagram shows the electric field lines due to two parallel metal plates. We conclude that
a proton at X would experience the same force if were placed at Y
An uncharged metal sphere will
be attracted by a charged metal surface.
A thin bar of length L is placed along the x-axis as shown in the figure. The bar is charged with a non-uniform charge density that can be described as (x) = cx2, where c is a constant. Find the magnitude of the electric field at x=0.
cLk
A parallel-plate air capacitor is connected to a constant-voltage battery. If the separation between the capacitor plates is doubled while the capacitor remains connected to the battery, the energy stored in the capacitor
drops to half its previous value.
Three charges, +q, +Q, and -Q, are placed at the corners of an equilateral triangle as shown in Figure 22-29. The net force on charge +q due to the other two charges is
horizontal to the right.
A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a uniform charge distribution totaling +Q and the hollow sphere a charge of -Q, the electric field at a radius r, where a < r < b, is which of the following in terms of k =1/(4 0)?
kQ/r2
In the Figure below, a charged particle (either an electron or a proton) is moving rightward between two parallel charged plates separated by distance d = 2.12 mm. The plate potentials are V1 = -60 V and V2 = -40 V. The particle is slowing down from an initial speed of 97 km/s at the left of the plate. Is the particle an electron or a proton? What is the speed (in km/s) just as it reaches the second plate?
proton; 74.6
Two charged metal spheres are connected by a wire, and sphere A is larger than sphere B as shown. The magnitude of the electric potential of sphere A is
the same as that at the surface of sphere B.
A uniformly charged thin non-conducting shell (hollow sphere) of radius R with a positive charge Q is placed a distance d from an infinite non-conducting sheet carrying a uniformly distributed charge density . The distance d is measured the center of the shell (point O). What is the magnitude of the total electric field at the center of the shell?
ó/2E0
