Q: Ampère’s Law relates the line integral of the magnetic field around a closed curve to the total current passing through the area bounded by the curve. Which equation represents Ampère’s Law?

$$\oint \vec{B} \cdot d\vec{s} = \mu_0$ I_{\text{enc}}$$

Q: The magnetic force on a moving charge $$q$$ with velocity $$\vec{v} in a $$magnetic field $$\vec{B} is $$given by which equation?

$$\vec{F} = q \vec{v} \times \vec{B}$$

Question 1

Which of the following correctly expresses the length $$l of a $$curved line from point $$i to $$point $$f$$ using a line integral?

Accepted Answer

$$l = \sum_k \Delta s_k \rightarrow \int_i^f ds$$

Question 2

If a magnetic field $$\vec{B} is $$everywhere perpendicular to a line, what is the value of the line integral $$\int \vec{B} \cdot d\vec{s}$$ along that line?

Accepted Answer

$$\int \vec{B} \cdot d\vec{s} = 0$$

Question 3

Ampère’s Law relates the line integral of the magnetic field around a closed curve to the total current passing through the area bounded by the curve. Which equation represents Ampère’s Law?

Accepted Answer

$$\oint \vec{B} \cdot d\vec{s} = \mu_0$ I_{	ext{enc}}$$

Question 4

A solenoid has $$N$$ turns per unit length and carries a current $$I. $$What is the magnitude of the magnetic field inside an ideal, infinitely long solenoid?

Accepted Answer

$$B = \mu_0$ n I$$

Question 5

Solenoid 2 has twice the diameter, twice the length, and twice as many turns as solenoid 1. 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 6

Which of the following statements about the magnetic field inside and outside an ideal, infinitely long solenoid is correct?

Accepted Answer

The magnetic field is uniform inside and zero outside.

Question 7

A long wire carries a current $$I. $$What is the direction of the magnetic field produced by the wire at a point located above the wire?

Accepted Answer

The magnetic field circles the wire according to the right-hand rule.

Question 8

A charged particle at rest in a magnetic field experiences which of the following?

Accepted Answer

No magnetic force.

Question 9

The magnetic force on a moving charge $$q$$ with velocity $$\vec{v} in a $$magnetic field $$\vec{B} is $$given by which equation?

Accepted Answer

$$\vec{F} = q \vec{v} 	imes \vec{B}$$

Question 10

A proton is shot straight at the center of a long, straight wire carrying current into the screen. What will happen to the proton?

Accepted Answer

It will be deflected over the wire.

Question 11

What is the radius $$r of $$the cyclotron orbit for a particle of mass $$m$$, charge $$q$$, and speed $$v in a $$uniform magnetic field $$B$$?

Accepted Answer

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

Question 12

Which of the following best describes the motion of a charged particle in a uniform magnetic field when its velocity is not perpendicular to the field?

Accepted Answer

It spirals around the magnetic field lines in a helical trajectory.

Question 13

If two parallel wires carry currents in the same direction, what is the nature of the force between them?

Accepted Answer

They attract each other.

Question 14

A current-carrying wire is placed perpendicular to a uniform magnetic field. What is the direction of the force on the wire?

Accepted Answer

In the direction given by the right-hand rule.

Question 15

A square current loop in a uniform magnetic field experiences a torque. What is the expression for the maximum torque $$	au on $$the loop?

Accepted Answer

$$	au = IAB$$

Question 16

Which of the following is true about the magnetic field outside a solenoid?

Accepted Answer

It resembles the field of a bar magnet.

Question 17

What is the effect of increasing the number of turns per unit length $$n in a $$solenoid, while keeping the current $$I$$ constant?

Accepted Answer

The magnetic field inside the solenoid increases.

Question 18

A charged particle moves parallel to a magnetic field. What is the magnetic force acting on it?

Accepted Answer

Zero.

Question 19

Which of the following best describes the direction of the magnetic force on a moving charge in a magnetic field?

Accepted Answer

Perpendicular to both the velocity and the magnetic field.

Line Integrals, Ampère’s Law, Solenoids, and Magnetic Forces: Study Notes

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