PH 106 Final Review
A certain capacitor, in series with a resistor, is being charged. At the end of 10 ms its charge is half the final value. The time constant for the process is about:
14 ms (qf=exp^(-t/(RC)), RC is τ (time constant))
A wire with a length of 150 m and a radius of 0.15 mm carries a current with a uniform current density of 2.8 × 107 A/m2. The current is:
2 A (J=I/A=I/(pi*r^2))
Resistances of 2.0 Ω, 4.0 Ω, and 6.0 Ω and a 24-V battery are all in series. The current in the 2.0 Ω resistor is:
2 A (series R=R1+R2, I=V/R)
Two large insulating parallel plates carry positive charge of equal magnitude that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest.
2 and 3 tie, then 1 and 4 tie, then 5 (draw lines away from positive for both bars, middle cancel, outside 2x)
A conducting sphere of radius 5.0 cm carries a net charge of 7.5 µC. What is the surface charge density on the sphere?
2.4e-4 (σ = Q / 4*π*r2)
The equivalent resistance between points 1 and 2 of the circuit shown is:
2.5 (series: Rt=R1+R2, parallel: 1/Rt=1/R1+1/R2, work from farthest away to closest)
An 8.0-mH inductor and a 2.0-Ω resistor are wired in series to an ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. The current reaches half its final value at a time of:
2.8ms (I(t)=I(1-e^(-Rt/L))
In the diagram, the current in the 3-Ω resistor is 4 A. The potential difference between points 1 and 2 is (3Ω and 2Ω resistors in series):
20 V (series I=constant, R=R1+R2, V=IR)
When a piece of paper is held with one face perpendicular to a uniform electric field the flux through it is 25 N⋅m2/C. When the paper is turned 25° with respect to the field the flux through it is:
23 (net flux=(Flux)(cosθ))
An LC circuit consists of a 1 μF capacitor and a 4 mH inductor. Its oscillation frequency is approximately:
2500 Hz (f=1/(2π√(LC)))
A sinusoidal electromagnetic wave has an electric field whose rms value is 100 V/m. What is the intensity I for this wave?
27 W/m^2 (S=ℇE^2c=E_RMS^2/μc)
10 C of charge are placed on a spherical conducting shell. A particle with a charge of -3C is placed at the center of the cavity. The net charge on the outer surface of the shell is:
+7 C
The work required to carry a particle with a charge of 6.0-µC from a 5.0-V equipotential surface to a 6.0-V equipotential surface and back again to the 5.0-V surface is:
0 (Work=(potential difference*charge), potential difference=(final-initial))
A certain resistor dissipates 0.5 W when connected to a 3 V potential difference. When connected to a 1 V potential difference, this resistor will dissipate:
0.056 V (P=V^2/R, resistance stays the same in the resistor)
Each of the three 25-μF capacitors shown is initially uncharged. How much charge in coulombs pass through the ammeter A after the switch S is closed?
0.3 C (parallel; Ct=C1+C2, Q=CtV)
Four 20-Ω resistors are connected in parallel and the combination is connected to a 20-V emf device. The current in the device is:
0.5 (parallel: 1/Rt=1/R1+1/R2, V=IR)
Each of the four capacitors shown is 500 μF. The voltmeter reads 1000V. The magnitude of the charge on each capacitor plate is:
0.5 C (Ct=C1+C2+C3+C4, Q=CtV, q1=q2=qi, qi=Q/4)
Three possible configurations for an electron e and a proton p are shown below. Take the zero of potential to be at infinity and rank the three configurations according to the potential at S, from most negative to most positive.
1 and 2 tie, 3 (look at distance of e compared to p in relation to S, e closer it is stronger than p and vice versa)
The current in the 5.0-Ω resistor in the circuit shown is:
1.5 A (combine all to get overall A, then split them to go through one branch or the other, current constant in series)
A tiny sphere carrying a charge of 6.5 µC sits in an electric field, at a point where the electric potential is 240 V. What is the sphere's potential energy?
1.6e-3 (potential energy=(potential*charge))
An 8.0-mH inductor and a 2.0-Ω resistor are wired in series to a 20-V ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. After a long time the current in the resistor and the current in the inductor are:
10 A, 10 A (I=V/R, since in series inductor and resistor would have the same value)
The light intensity 10 m from a point source is 1000 W/m2. The intensity 100 m from the same source is:
10 W/m^2 (I=I_initial/d^2)
A concave spherical mirror has a focal length of 12 cm. If an object is placed 6 cm in front of it the image position is:
12 cm behind the mirror (1/u+1/v=1/f, review whether + or - each for concave or convex)
The index of refraction of benzene is 1.80. The Brewster's angle at a benzene-air interface is about:
29 (θb=tan^-1(n2/n1))
Two identical capacitors, each with capacitance C, are connected in parallel and the combination is connected in series to a third identical capacitor. The equivalent capacitance of this arrangement is:
2C/3 (series: 1/Ct=1/C1+1/C2, parallel: Ct=C1+C2)
Complete the following statement: According to today's scientists, magnetic monopoles
do not exist anywhere in the universe
Faraday's law states that an induced emf is proportional to:
the rate of change of the magnetic flux (e = -dφ/dt)
A 120-V power line is protected by a 15-A fuse. What is the maximum number of 120 V, 500 W light bulbs that can be operated at full brightness from this line?
3 (nP=VI, round down because if it over they do not operate at full brightness anymore)
Two long straight current-carrying parallel wires cross the x axis and carry currents I and 3I in the same direction, as shown. At what value of x is the net magnetic field zero?
3 (need B1=B2, distance from 3I current is triple the distance from the 1I current)
The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r) and radial lengths. The circuits carry the same current. Rank them according to the magnitudes of the magnetic fields they produce at C, least to greatest.
3, 2, 1 (least close, semi-circle, fully enclosed; B=μIφ/(4πr)
Light with an intensity of 1 kW/m2 falls normally on a surface with an area of 1 cm2 and is completely absorbed. The force of the radiation on the surface is:
3.3e-10 N (for complete absorption F=PA, P=I/c)
The index of refraction of benzene is 1.80. The critical angle for total internal reflection, at a benzene-air interface, is about:
34 degrees (θc=sin^-1(1/n))
The diagram shows six 6-μF capacitors (3 in series connected in parallel to another 3 in series). The capacitance in μF between points a and b is:
4 (series: 1/Ct=1/C1+1/C2, parallel Ct=C1+C2)
A convex spherical mirror has a focal length of 12 cm. If an object is placed 6 cm in front of it the image position is:
4 cm behind the mirror (1/u+1/v=1/f, review whether + or - each for concave or convex)
The flux of the electric field (24 N/C)i + (30 N/C)j + (16 N/C)k through a 2.0 m2 portion of the yz plane is
48 (flux of E would be perp to YZ plane, so used X component, flux is EA)
An isolated charged point particle produces an electric field with magnitude E at a point 2 m away. At a point 1 m from the particle the magnitude of the field is:
4E bc factor of 1/r^2
Two long straight wires are parallel and carry current in the same direction. The currents are 8.0 and 12 A and the wires are separated by 0.40 cm. The magnetic field at a point midway between the wires is:
4e-4 T (since traveling in same way- repulsive so subtract, B=μI/(2πr)
A 2.0 T uniform magnetic field makes an angle of 30° with the z axis. The magnetic flux through a 3.0 m2 portion of the xy plane is:
5.2 Wb (Φ =BAcosθ)
A wire is 1 m long and 1 × 10-6 m2 in cross-sectional area. When connected to a potential difference of 2 V, a current of 4 A exists in the wire. The resistivity of this wire is:
5e-7 (R=ρl/A=V/I)
A 3-cm high object is in front of a thin lens. The object distance is 4 cm and the image distance is -8 cm. The image height is:
6 cm (m=-q/p=h_i/h_o, m=mag, q=image dis, p=object dis, h_i=image height, h_o=object height)
A rod with resistance R lies across frictionless conducting rails in a constant uniform magnetic field B, as shown. Assume the rails have negligible resistance. The magnitude of the force that must be applied by a person to pull the rod to the right at constant speed v is:
B^2L^2v/R (ℇ=BLv=IR, F=BIL, combine and rearrange)
Radio receivers are usually tuned by adjusting the capacitor of an LC circuit. If C = C1 for a frequency of 600 kHz, then for a frequency of 1200 kHz one must adjust C to:
C1/4 (f=1/(2π√(LC)))
Which one of the following is not one of Maxwell's fundamental equations of electromagnetism?
Coulomb's Law
The electric potential at a certain point is given by V = -7.5x2 + 3x, where V is in volts and x is in meters. What is the electric field at that point?
E=(15x-3)i (E=-dV/dx)
A conducting sphere with radius R is charged until the magnitude of the electric field just outside its surface is E. The electric potential of the sphere, relative to the potential for away, is:
ER (E=kq/r^2, V=kq/r, q combine to get in terms of E and r)
Two point charges are arranged as shown. In which region could a third charge +1 C be placed so that the net electrostatic force on it is zero?
I only (point lines in or out based on sign and see which ones cancel out direction wise and then magnitude wise)
In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit (I, II, III, IV, V) will the bulbs glow with the same brightness as in circuit X?
IV (looking for same current (associated with brightness), bulbs are resistors and EMF is voltage)
Charge Q is distributed uniformly throughout a spherical insulating shell. The net electric flux through the outer surface of the shell is:
Q/ε0 (equation for flux)
A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time, after t = 0 that the energy stored in the magnetic field of the inductor is a maximum is:
T/4 (T=0 fully capacitor, T/4 fully inductor, T/2 fully capacitor, 3T/4 fully inductor)
A parallel plate capacitor is being charged by a constant current i. During the charging, the electric field within the plates is increasing with time. Which one of the following statements concerning the magnetic field between the plates is true?
The induced magnetic field strength is zero tesla near the center of the plates and increases as r increases toward the edges of the plates
Which of the following choices concerning the net magnetic flux through any enclosed surface is true according to Gauss' law for magnetic fields?
The magnetic flux equals zero.
What is a displacement current?
a fictitious current across the plates of a capacitor
What is produced from a changing electric field?
a magnetic field directed perpendicularly to the changing field
A long straight cylindrical shell carries current i uniformly distributed over its cross section. The magnitude of the magnetic field is greatest:
at the outer surface of the shell (mag field inversely proportional to distance from surface)
When light travels from medium X to medium Y as shown (angle with normal decreases from X to Y):
both the speed and the wavelength decrease (frequency remains the same, speed and wavelength directly related)
If the speed of light is c, and the index of refraction of a material is n, what is the speed of light in the material?
c/n
A car battery is rated at 80 A⋅h. An ampere-hour is a unit of:
charge
A 2-μF and a 1-μF capacitor are connected in series and a potential difference is applied across the combination. The 2-μF capacitor has:
charge conserved, half the potential difference as the other capacitor (C1V1=C2V2)
The electric field in a region around the origin is given by C(xi+yj) , where C is a constant. The equipotential surfaces are:
concentric cylinders with axes along the z axis (perp to xy)
A long straight wire is in the plane of a rectangular conducting loop. The straight wire initially carries a constant current i in the direction shown. While the current i is being shut off, the current in the loop is:
counterclockwise (want to keep magnetic flux the same)
A solid insulating sphere of radius R contains a positive charge that is distributed with a volume charge density that does not depend on angle but does increase linearly with distance from the sphere center. Which of the graphs below correctly gives the magnitude E of the electric field as a function of the distance r from the center of the sphere?
curve up to peak, curve down after peak (volume charge density does not depend on angle, increase linearly with distance from sphere center)
Positive charge +Q is uniformly distributed on the upper half of a semicircular rod and negative charge -Q is uniformly distributed on the lower half. In what direction does the electric field vector point at P, the center of the semicircle?
down (+ points towards P, - points away from P, left and right cancel out so its only down)
Four long straight wires carry equal currents into the page as shown. The direction of the magnetic force exerted on wire F is (F is left wire, with one on right, one on top, one on bottom):
east (all same direction means all attract, top and bottom cancel out so just east force)
An electron and a proton are both initially moving with the same speed and in the same direction at 90˚ to the same uniform magnetic field. They experience magnetic forces, which are initially:
equal in magnitude but opposite in direction
A virtual image is one:
from which light rays diverge but do not pass through
This figure shows a junction. What is true of the currents?
i==i1+i2
A magnetic field exerts a force on a charged particle:
if the particle is moving across the field lines
The electric field for a plane electromagnetic wave traveling in the +y direction is shown. Consider a point where E is in the +z direction. The B field is:
in the +x direction and in phase with the E field (perp to E and v, always in phase with E)
The figure shows a bar moving to the right on two conducting rails. To make an induced current i in the direction indicated, a constant magnetic field between the rails should be in what direction?
into the page (need to counteract change occurring by the increase of A from moving v)
An upright object placed outside the focal point of a converging lens will produce an image that is:
inverted and real
An electrically charged object creates an electric field. The electric potential due to this object:
is a scalar but will be positive or negative depending on the sign of the charge (electric potential is V=kq/r, no direction)
The electric flux Φ through a surface
is the amount of electric field piercing the surface
The diagrams below depict four different charge distributions. The charged particles are all the same distance from the origin. The electric field at the origin:
is zero for situation 4 (cancel out on both x and y axis)
Let k denote 1/4πε0. The magnitude of the electric field at a distance r from an isolated point charge q is:
kq/r^2
The magnetic torque exerted on a flat current-carrying loop of wire by a uniform magnetic field B is:
maximum when the plane of the loop is parallel to B (proportional to sine so want parallel for max)
Two conducting spheres are far apart. The smaller sphere carries a total charge of Q. The larger sphere has a radius that is twice that of the smaller and is neutral. After the two spheres are connected by a conducting wire, the charges on the smaller and larger spheres, respectively, are:
q1=Q/3, q2=2Q/3 (r2=2r1, q2=2q1, Q=q1+q2=q1+2q1=3q1)
A particle with mass m and charge -q is projected with speed v0 into the region between two parallel plates as shown. The potential difference between the two plates is V and their separation is d. The change in kinetic energy of the particle as it traverses this region is:
qV (W=qV=KE)
Consider radio waves (r), visible light (v), infrared (i), X rays (x), and ultraviolet (u). In order of increasing frequency, they are:
r, i, v, u, x
A uniform magnetic field is directed into the page. A charged particle, moving in the plane of the page, follows a clockwise spiral of decreasing radius as shown. A reasonable explanation is:
r=mv/Bq (radius smaller so slowing down, clockwise means negative)
The emf developed in a coil X due to the current in a neighboring coil Y is proportional to the:
rate of change of magnetic field in X (changing magnetic field is what causes the induction)
Gauss's law
relates the electric field at points on a closed surface to the net charge enclosed by that surface
As an object is moved from a distant location toward the center of curvature of a concave mirror its image:
remains real and becomes larger (in concave mirror- object inside focal point--> magnified/virtual, object beyond focal point-->image is real)
If the image distance is negative:
the image is virtual
The circuit shown was wired for the purpose of measuring the resistance of the lamp L. Inspection shows that:
the meters, V and A, should be interchanged (V measures voltage drop so in parallel, A measures current through so in series)
Capacitors C1 and C2 are connected in parallel and a potential difference is applied to the combination. If the capacitor that is equivalent to the combination has the same potential difference, then the charge on the equivalent capacitor is the same as:
the sum of the charges on C1 and C2 (Ct=C1+C2)
In the experiment shown: (one circuit with switch, second circuit with G)
there is current in G just after S is opened or closed (induction)
An electric field is associated with every:
time-dependent magnetic field (E=(r/2)*(dB/dt))
The magnetic field lines inside the solenoid shown are:
toward the top of the page (RHR)
What would you get if you took a bar magnet and cut it in half?
two shorter magnets, each with a north pole and a south pole
If both the resistance and the inductance in an LR series circuit are doubled the new inductive time constant will be:
unchanged (τ = L/R)
The diagram shows a straight wire carrying a flow of electrons into the page. The wire is between the poles of a permanent magnet. The direction of the magnetic force exerted on the wire is:
up (pointer direction of index, middle magnetic field, thumb magnetic force, force opposite because it is an electron)
The figure shows a uniform magnetic field B directed to the left and a wire carrying a current into the page. The direction of the magnetic force acting on the wire is:
up (pointer is current, middle finger is B, thumb is force)
The current is from left to right in the conductor shown. The magnetic field is into the page and point S is at a higher potential than point T. The charge carriers are:
upward
An electron enters a region of uniform perpendicular E and B fields. It is observed that the velocity of the electron is unaffected. A possible explanation is:
v is perpendicular to both E and B and has magnitude E/B
The separation of white light into colors by a prism is associated with:
variation of index of refraction with wavelength
An object is 2 m in front of a plane mirror. Its image is:
virtual, upright, and 2 m behind the mirror (Plane mirror form virtual images at same distance behind the mirror as the object distance)
A 2-μF and a 1-μF capacitor are connected in parallel and a potential difference is applied across the combination. The 2-μF capacitor has:
voltage conserved, twice the charge as the other capacitor
In the context of the loop and junctions rules for electrical circuits a junction is:
where three or more wires are joined
A wire carrying a charge density of λ C/m is bent into a circle of radius r. What is the electric potential at the center of the circle?
λ/2ε0
A long line of charge with λℓ charge per unit length runs along the cylindrical axis of a cylindrical conducting shell which carries a charge per unit length of λc. The charge per unit length on the inner and outer surfaces of the shell, respectively are:
−λℓ and λc + λℓ (inner; outer, conserves charge)
