Q: The magnetic field at a point due to a moving charge is given by the Biot-Savart law. Which equation correctly expresses the magnitude of the magnetic field at a distance $$r$$ from a charge $$q$$ moving with velocity $$v at an $$angle $$\theta$$?

$$B = \frac{\mu_0$}{4\pi} \frac{qv \sin \theta}{r^2$}$$

Q: A solenoid with 3000 windings, length $$0.35\,\text{m}$$, and magnetic field $$0.27\,\text{T} is $$used. What is the current in the windings? ($$\mu_0$ = 1.26 \times 10$$^{-6}$$\,\text{T}\cdot\text{m}/\text{A})$$

$$I = 0.27 / (1.26 \times 10$$^{-6}$$ \times 8570)$$

Q: The torque on a magnetic dipole $$\vec{m} in an $$external magnetic field $$\vec{B} is $$given by which equation?

$$\vec{\tau} = \vec{m} \times \vec{B}$$

Question 1

A vertical wire carries current upward through the center of a horizontal table. A compass rests on the table near the wire. Which direction will the north pole of the compass point?

Accepted Answer

Tangential to the circle centered on the wire, following the right-hand rule

Question 2

The magnetic field at a point due to a moving charge is given by the Biot-Savart law. Which equation correctly expresses the magnitude of the magnetic field at a distance $$r$$ from a charge $$q$$ moving with velocity $$v at an $$angle $$	heta$$?

Accepted Answer

$$B = \frac{\mu_0$}{4\pi} \frac{qv \sin 	heta}{r^2$}$$

Question 3

Two parallel wires carry equal currents in opposite directions. What is the direction of the force on the left wire due to the right wire?

Accepted Answer

To the left

Question 4

A solenoid with 3000 windings, length $$0.35\,	ext{m}$$, and magnetic field $$0.27\,	ext{T} is $$used. What is the current in the windings? ($$\mu_0$ = 1.26 	imes 10$$^{-6}$$\,	ext{T}\cdot	ext{m}/	ext{A})$$

Accepted Answer

$$I = 0.27 / (1.26 	imes 10$$^{-6}$$ 	imes 8570)$$

Question 5

A loop of wire moves to the right and enters a region with a uniform magnetic field directed into the page. At the instant the loop is fully inside the field, what is the direction of the induced current?

Accepted Answer

No current

Question 6

The torque on a magnetic dipole $$\vec{m} in an $$external magnetic field $$\vec{B} is $$given by which equation?

Accepted Answer

$$\vec{	au} = \vec{m} 	imes \vec{B}$$

Question 7

A wire of length $$l$$ carrying current $$I is $$placed in a magnetic field $$B$$ perpendicular to the wire. What is the magnitude of the force on the wire?

Accepted Answer

$$F = IlB \sin \alpha$$

Question 8

A rectangular loop of width $$w$$ and height $$h$$ moves to the right at constant speed $$v$$ and enters a region of uniform magnetic field $$B. $$What is the induced emf while the loop is entering the field?

Accepted Answer

$$\mathcal{E} = Bhv$$

Question 9

A loop of area $$A is $$rotated at constant angular speed $$\omega in a $$uniform magnetic field $$B. $$What is the expression for the induced emf?

Accepted Answer

$$\mathcal{E} = BA\omega \sin \omega t$$

Question 10

A uniform magnetic field is directed out of the page and has a circular cross section of radius $$R. $$The magnitude of the magnetic field increases at a steady rate. What is the direction of the induced electric field at point P?

Accepted Answer

To the right

Question 11

Which of the following is true about the magnetic field at the center of a coil of radius $$R$$ with $$N$$ turns carrying current $$I$$?

Accepted Answer

$$B = \frac{\mu_0$}{2} \frac{NI}{R}$$

Question 12

A charged particle moves in a circle in a uniform magnetic field. What is the expression for the radius of the circle?

Accepted Answer

$$r = \frac{mv}{qB}$$

Question 13

A parallel plate capacitor is charging. Consider three concentric circular surfaces with radii $$3R/2$$, $$R$$, and $$R/2. $$Rank the electric flux through these surfaces from least to greatest.

Accepted Answer

Surface with $$R/2$$ \u003c Surface with $$R = $$Surface with $$3R/2$$

Question 14

Which of the following statements about the displacement current in a parallel plate capacitor is correct?

Accepted Answer

The displacement current equals the conduction current for the curved surface

Question 15

Which equation describes the induced emf in a loop due to a changing magnetic flux?

Accepted Answer

$$\mathcal{E} = \frac{d\Phi_m}{dt}$$

Question 16

Which of the following is NOT a circuit element commonly found in basic circuit diagrams?

Accepted Answer

Transistors

Question 17

Kirchoff’s junction rule states:

Accepted Answer

The current into a junction is equal to the current out of the junction

Question 18

Kirchoff’s loop rule states:

Accepted Answer

The sum of all potential differences around a loop must equal zero

Magnetic Fields, Forces, and Electromagnetic Induction: Study Notes

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