Question 1

A conducting loop of radius $$r is $$placed in a region where the magnetic field $$B is $$increasing into the page. According to Faraday's Law, what is the direction of the induced electric field inside the loop?

Accepted Answer

Clockwise around the loop

Question 2

Which of the following correctly expresses the magnitude of the induced emf ($$\varepsilon) $$around a closed path due to a changing magnetic flux $$\Phi_B$$?

Accepted Answer

$$\varepsilon = -\frac{d\Phi_B}{dt}$$

Question 3

A circular loop of radius $$r is in a $$region where the magnetic field $$B is $$increasing at a constant rate. What is the magnitude of the induced electric field at a distance $$r$$ from the center?

Accepted Answer

$$E = \frac{1}{2} r \frac{dB}{dt}$$

Question 4

A solenoid has a radius $$r$$ and $$n$$ turns per unit length. If the current through the solenoid increases from $$0 to$$ $$I in $$time $$\Delta t$$, what is the magnitude of the induced electric field at a distance $$r$$ from the axis (inside the solenoid)?

Accepted Answer

$$E = \mu_0$ n \frac{I}{\Delta t} r$$

Question 5

Which statement best describes the work done in moving a charge around a closed loop in the presence of an induced electric field from a changing magnetic field?

Accepted Answer

The work done is not zero because the induced electric field is non-conservative.

Question 6

A circular metal loop is pulled to the right through a uniform magnetic field directed away from you (out of the page). The loop does not exit the field. What is the direction of the induced current?

Accepted Answer

No current is induced

Question 7

A triangular aluminum loop is slowly entering a region with a uniform magnetic field directed away from you. What is the direction of the induced current as the loop enters the field?

Accepted Answer

Clockwise

Question 8

A triangular aluminum loop is slowly exiting a region with a uniform magnetic field directed away from you. What is the direction of the induced current as the loop exits the field?

Accepted Answer

Counterclockwise

Question 9

A conducting bar slides to the right on conducting rails in a uniform magnetic field directed perpendicular to the plane. What happens to the magnetic flux through the loop as the bar moves?

Accepted Answer

The magnetic flux increases

Question 10

A voltmeter is connected to a coil of wire. A magnet is stationary near the coil with its south end close to the coil. The meter indicates a current flowing from left to right. What is wrong with this scenario?

Accepted Answer

Current should be flowing from right to left

Question 11

Which of the following is a correct statement of Faraday's Law in integral form?

Accepted Answer

$$\oint \vec{E} \cdot d\vec{s} = -\frac{d\Phi_B}{dt}$$

Question 12

If the magnetic field inside a circular loop is decreasing, what is the direction of the induced current?

Accepted Answer

Counterclockwise

Question 13

A solenoid 2 has twice the diameter, twice the length, and twice as many turns as solenoid 1. The same current $$I is $$passed through both solenoids. How does the field $$B_2 at $$the center of solenoid 2 compare to $$B_1 at $$the center of solenoid 1?

Accepted Answer

$$B_2$$ = $$B_1$$

Question 14

Which of the following is NOT a consequence of a non-conservative induced electric field?

Accepted Answer

The induced electric field can be described by a potential function everywhere

Question 15

A circular loop of radius $$r is $$placed in a region where the magnetic field $$B is $$decreasing out of the page. What is the direction of the induced current?

Accepted Answer

Clockwise

Question 16

Which equation gives the induced electric field at a distance $$r$$ from the center of a region with a time-varying magnetic field $$B ($$for $$r$$ inside the region)?

Accepted Answer

$$E = \frac{r}{2} \frac{dB}{dt}$$

Question 17

A proton is located at $$(1\ \mathrm{cm}, 1\ \mathrm{cm}) in $$the $$x$$-$$y$$ plane and is moving at $$2.0 	imes 10^7$\ \mathrm{m/s} in $$the $$x$$ direction. What is the direction of the associated magnetic field at position $$(1\ \mathrm{cm}, -1\ \mathrm{cm})$$?

Accepted Answer

Magnetic field points into the page and its magnitude is increasing

Question 18

Which of the following best describes the relationship between the induced emf and the rate of change of magnetic flux through a loop?

Accepted Answer

The induced emf is proportional to the rate of change of magnetic flux

Induced Electric Fields and Faraday’s Law: Study Notes

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