Physics 208

Infinite line of charge: A long, thin rod parallel to the y-axis is located at x = -1.0 cm and carries a uniform linear charge density of +1.0 nC/m. A second long, thin rod parallel to the z-axis is located at x = +1.0 cm and carries a uniform linear charge density of -1.0 nC/m. What is the net electric field due to these rods at the origin? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

(3.6 × 103 N/C) (i) hat

Charge on conductors: A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries a net excess charge of -500 nC. A point charge of +300 nC is present at the center. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C) The radial component of the electric field at a point that is 0.60 m from the center is closest to

+7500 N/C.

Force on moving charges: A uniform magnetic field of magnitude 0.80 T in the negative z direction is present in a region of space, as shown in the figure. A uniform electric field is also present and is set at 76,000 V/m in the +y direction. An electron is projected with an initial velocity v0 = 9.5 × 104 m/s in the +x direction. The y component of the initial force on the electron is closest to which of the following quantities? (e = 1.60 × 10-19 C) Short Description: An electron is moving with a velocity v subscript 0 towards right and a magnetic field B equals 0.80 T moves into the page an x y plane is shown to the top right for reference.

-2.4 × 10-14 N

Constant electric field vector downwards E everywhere in space (a large flat plane of charge creates this potential) you hold a positively charged particle so that it is stationary. What force are you applying?

-qEy(hat) (negative for a downward vector)

Electric field and potential: If the potential in a region is given by V(x,y,z) = xy - 3z-2, then the y component of the electric field in that region is

-x

Two points in space have electric potential V(A) = 20 volts and V(B) = 100 volts. How much work does it take to move a 10 uC charge from A to B

.8 mJ

Potential energy of a current loop: A rigid circular loop has a radius of 0.20 m and is in the xy-plane. A clockwise current I is carried by the loop, as shown. The magnitude of the magnetic moment of the loop is 0.75 A ∙ m2. A uniform external magnetic field, B = 0.20 T in the positive x-direction, is present. An external torque changes the orientation of the loop from one of lowest potential energy to one of highest potential energy. The work done by this external torque is closest to

0.30J

A closed loop conductor that forms a circle with a radius of 2.0 m is located in a uniform but changing magnetic field. If the maximum emf induced in the loop is 5.0 V, what is the maximum rate at which the magnetic field strength is changing if the magnetic field is oriented perpendicular to the plane in which the loop lies?

0.40 T/s

A series LR circuit consists of a 2.0-H inductor with negligible internal resistance, a 100-ohm resistor, an open switch, and a 9.0-V ideal power source. After the switch is closed, what is the maximum power delivered by the power supply?

0.81 W

A 4.0-μF capacitor is connected in series with a 7.0 MΩ resistor, and this combination is connected across an ideal 10-V DC battery. What is the current in the circuit when the capacitor has reached 40% of its maximum charge?

0.86 μA

The figure shows the cross-section of a hollow cylinder of inner radius a = 5.0 cm and outer radius b = 7.0 cm. A uniform current density of 1.0 A/ cm2 flows through the cylinder parallel to its axis. Calculate the magnitude of the magnetic field at a distance of d = 10 cm from the axis of the cylinder. (μ0 = 4π × 10-7 T ∙ m/A)

1.5 × 10-4 T

The figure shows the cross-section of a hollow cylinder of inner radius a = 5.0 cm and outer radius b = 7.0 cm. A uniform current density of 1.0 A/ cm2 flows through the cylinder parallel to its axis. Calculate the magnitude of the magnetic field at a distance of d = 10 cm from the axis of the cylinder. (μ0 = 4π × 10-7 T ∙ m/A) Short Description: A cross section of a hollow cylinder with an inner radius of a and an outer radius of b. A distance d is shown with a dashed arrow pointed horizontally towards left.

1.5 × 10-4 T

A solenoid of length 18 cm consists of closely spaced coils of wire wrapped tightly around a wooden core. The magnetic field strength is 2.0 mT inside the solenoid near its center when a certain current flows through the coils. If the coils of the solenoid are now pulled apart slightly, stretching it to 21 cm without appreciably changing the size of the coils, what does the magnetic field become near the center of the solenoid when the same current flows through the coils? (μ0 = 4π × 10-7 T ∙ m/A)

1.7 mT

At what rate would the current in a 100-mH inductor have to change to induce an emf of 1000 V in the inductor?

10,000 A/s

A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). If the sphere's radius were twice as large, and the charge on the sphere was double, what would be the potential on the surface relative to infinity?

100 V

A solenoid of length 0.700 m having a circular cross-section of radius 5.00 cm stores 6.00 µJ of energy when a 0.400-A current runs through it. What is the winding density of the solenoid? (μ0 = 4π × 10-7 T ∙ m/A)

104 turns/m

A 110-V hair dryer is rated at 1200 W. What current will it draw when operating from a 110-V electrical outlet?

11 A

Energy in capacitors: A 6.00-μF parallel-plate capacitor has charges of ±40.0 μC on its plates. How much potential energy is stored in this capacitor?

133 μJ

Resistivity: What length of a certain metal wire of diameter 0.15 mm is needed for the wire to have a resistance of 15 Ω? The resistivity of this metal is 1.68 × 10-8 Ω ∙ m.

16 m

RC circuits: An uncharged 1.0-μF capacitor is connected in series with a 23-kΩ resistor, an ideal 7.0-V battery, and an open switch. What is the voltage across the capacitor 11 ms after closing the switch?

2.7 V

A single point charge is at the origin, with electric potential relative to infinity of V = kQ/r. How much work must you do to move a 4 uC particle from point A to point B. V(A) = 10 V 3 cm from the origin and B is 2cm from the origin.

20 uJ

Coulomb's law: A 1.0-C point charge is 15 m from a second point charge, and the electric force on one of them due to the other is 1.0 N. What is the magnitude of the second charge? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

25 nC

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates. All the geometric parameters of the capacitor (plate diameter and plate separation) are now doubled and the charge is reduced by one half. If the original capacitance was C0, what is the new capacitance?

2C0

At a distance D from a very long (essentially infinite) uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 500 N/C?

2D

The capacitors in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance, Cab, of this capacitor network? One capacitor in a series with a parallel set of 3 capacitors, two in series and one parallel to the two.

3.0 µF

Potential due to point-charges: Three point charges of -2.00 μC, +4.00 μC, and +6.00 μC are placed along the x-axis as shown in the figure. What is the electrical potential at point P (relative to infinity) due to these charges? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

307 kV

A solenoid has a length of 10cm is composed of 100 loops and has a current of 1A circulating. What is the magnetic field inside far from the extremities

4pi10^-4 T

Electric field of a single point-charge: An atomic nucleus has a charge of +40e. What is the magnitude of the electric field at a distance of 1.0 m from the center of the nucleus? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2, e = 1.60 × 10-19 C)

5.8 × 10-8 N/C

As shown in the figure, a wire is bent into the shape of a tightly closed omega (Ω), with a circular loop of radius 4.0 cm and two long straight sections. The loop is in the xy-plane, with the center at the origin. The straight sections are parallel to the x-axis. The wire carries a 5.0-A current, as shown. What is the magnitude of the magnetic field at the center of the loop? (μ0 = 4π × 10-7 T ∙ m/A)

54 uT

In an LC circuit containing a 40-mH ideal inductor and a 1.2-mF capacitor, the maximum charge on the capacitor is 45 mC during the oscillations. What is the maximum current through the inductor during the oscillations?

6.5 A

In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y,z) = 3x2y2 + yz3 - 2z3x, where x, y, and z are measured in meters and V is in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0).

8.6 V/m

Which of the following statements about inductors are correct? An inductor always resists any change in the current through it. When it is connected in a circuit, an inductor always resists having current flow through it. When an inductor and a resistor are connected in series with a DC battery, the current in the circuit is reduced to zero in one time constant. Inductors store energy by building up charge. When an inductor and a resistor are connected in series with a DC battery, the current in the circuit is zero after a very long time.

An inductor always resists any change in the current through it

Two like sign charges can have a place or places with zero electric field. Where does this happen?

At a point directly between the charges

The figure shows three metal coils labeled A, B, and C heading towards a region where a uniform static magnetic field exists. The coils move with the same constant velocity and all have the same resistance. Their relative sizes are indicated by the background grid. As they enter the magnetic field the coils will have an induced electric current in them. For which coil will the current be the greatest?

C

You are given a copper bar of dimensions 3 cm × 5 cm × 8 cm and asked to attach leads to it in order to make a resistor. If you want to achieve the SMALLEST possible resistance, you should attach the leads to the opposite faces that measure A)3 cm × 5 cm. B)3 cm × 8 cm. C)5 cm × 8 cm. D)Any pair of faces produces the same resistance.

C

A number of charges are arranged in three cases as shown. Rank the cases from the largest magnitude net Coulomb force on the -3 μC charge to the smallest net Coulomb force on -3 μC charge. Case 1: -3 +1 -1 Case 2: -3 +1 Case 3: -3 +1.......-1

Case 2 > Case 3 > Case 1

Below are shown the motions of four charges in uniform electric fields. The polarity (+ or -) of the charges and the orientation of the E-fields are indicated in each case. Short description: Case 1: negative q moves in the direction of the electric field Case 2: q moves in the direction of the electric field and then moves back Case 3: q moves against the direction of the electric field Case 4: negative q moves against the direction of the electric field In which case does the charge LOSE the most potential energy from its initial position (the solid circle) to its final position (the dotted circle)?

Case 4

Lines of charge: At a distance D from a very long (essentially infinite) uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 2000 N/C?

D/2

What is the cause of the northern lights or Aurora Borealis

Electrically charged particles enter the magnetic field of the earth

Two equal negative charges are held in place at a fixed distance. If you put a third positive charge midway between these two charges, its electrical potential energy of the system (relative to infinity) is zero because the electrical forces on the third charge due to the two fixed charges just balance each other.

FALSE

Flux: If the electric flux through a closed surface is zero, the electric field at points on that surface must be zero.

False

Superposition of electric fields, two parallel equal and opposite infinite sheets of charge are arranged with positive on the left and negative on the right. Total electric field is superposition (sum of contributions from each). If point X is placed on the left of the positive plate what is the direction of the electric field at this point

Field is zero

What is the current a very long time after switch is closed?

I=0

Magnetic Dipole moment: a wire loop with current I (clockwise) is situated in the plane of the page. What is the direction of its magnetic dipole moment

Into page

Equal but opposite charges are connected by a rigid insulating rod. They are placed near a negative charge to the left of them nearer to the positive charge. What is the net force on the two connected charges?

Left

Magnetic force on a current carrying wire: Which orientation of the battery causes the bar to accelerate to the right, Image: B is into the page, two conducting rails with a conducting bar are attached to a battery, if F is to the right should the positive end of the battery be on top or bottom

On top

A certain electric field arises from a point charge. How does its direction depend on the sign of the point charge?

Positive - Away Negative - Towards

The total charge on a conductor shell is +5q. A point charge of +q is placed at the center. How is the charge distributed?

Q(inner_surface)= -q Q(outer_surface) = 6q Q(body)= 0 Is necessary for E=0 inside the conductor

Parallel-plate capacitors: The charge on the square plates of a parallel-plate capacitor is Q. The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. The amount of charge on the plates is now equal to

Q/2

The equipotentials get closer together nearer the charge because

The E field is bigger

RC circuits: An RC circuit is connected across an ideal DC voltage source through an open switch. The switch is closed at time t = 0 s. Which of the following statements regarding the circuit are correct? (There may be more than one correct choice.)

The current is maximum right after the switch is closed

Beams of protons can be used to irradiate and destroy tumors. How are magnetic fields used to make these beams?

The paths of protons are controlled using the Lorentz force

In the following uniform electric field, directed from left to right, three points of A, B, and C are shown. Which of the following statement about the electric potential is true? ——————————> A. C. E ——————————> B ——————————>

The potential at points A and B are equal, and the potential at point C is lower than the potential at point A.

What will happen to two parallel wires with current running in the same direction

The wires will attract each other

In the following figure two identical conductive neutral balls on an insulating stand, named as X and Y, are initially attached together. An insulator with excess positive charge is brought close to the balls. Then, the right sphere is moved away from the left one. Then the same process is repeated with a negative rod. Which of the following statements are true.

There is a repulsive force between the negative rod and sphere Y There is an attractive force between the positive rod and sphere X There is an attractive force between the negative rod and sphere X There is a repulsive force between the positive rod and sphere Y

Which bulb is brighter in a series where the two bulbs are identical?

They are the same

A Negative charge moves in a B field that goes into the page, the velocity is up, the direction of the Lorentz force is

Towards the right (invert the direction for negative particle, middle finger into the page and index finger up)

Two charges are arranged one positive, one negative on the x axis equal but opposite distances from the origin. What is the direction of the force on the positively charged particle on the y axis a +r from the origin from the two charges

Towards the side of the negative charge but the forces in the j (hat) direction are equal and opposite so they cancel.

Constant E-field everywhere in space F(coulomb) = qE, You hold a positive point charge in the field which points towards the right in what direction does the electric potential not change? ΔV = W/q, W= ∫ F(you)ds

Up and down

A battery is to be connected to a circuit so that when the switch is closed the compass needle (which is pointing up) deflects counter clockwise, which way should the battery be connected?

With the negative side close to the south end

Induction: X and Y are two uncharged metal spheres on insulating stands, and are in contact with each other. A positively charged rod R is brought close to X as shown in Figure (a). Short Description: Figure a. A positively charged rod R is brought to the left of the two metal spheres X and Y which are close to each other and are placed on top of insulating stands from left to right. Sphere Y is now moved away from X, as in Figure (b). Short Description: Figure b. A positively charged rod R is closer to the left of the metal sphere X which is attached to an insulating stand. A metal sphere Y is at a certain distance to the right of sphere X. What are the final charge states of X and Y?

X is negative and Y is positive

Coulomb's law: When two point charges are a distance d part, the electric force that each one feels from the other has magnitude F. In order to make this force twice as strong, the distance would have to be changed to

d/square root of (2)

What is the current through a loop including +i1 +i2 and -i3 where magnetic field is counterclockwise

i1+i2-i3

The long straight wire in the figure carries a current I that is decreasing with time at a constant rate. The circular loops A, B, and C all lie in a plane containing the wire(a above the wire b on the wire c below the wire and current flowing to the I). The induced emf in each of the loops A, B, and C is such that

loop A has a counter-clockwise emf, loop B has no induced emf, and loop C has a clockwise emf.

The figure shows two unequal point charges, q and Q, with both negative. Charge Q has greater magnitude than charge q. In which of the regions X, Y, Z will there be a point at which the net electric field due to these two charges is zero? ......q...........Q................ x. y. z

only region Y

Direction of magnetic fields: A horizontal wire carries a current straight toward you. From your point of view, the magnetic field at a point directly below the wire points

to the right