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AP Physics C: Electricity and Magnetism Practice Quiz: Ampère's Law

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 11 questions to check your progress.

Question 1 of 11

According to the provided text, Ampère's law describes the relationship between which two quantities?

All Questions (11)

According to the provided text, Ampère's law describes the relationship between which two quantities?

A) The electric field and the enclosed electric charge.

B) The magnetic force and the velocity of a charge carrier.

C) The magnitude of the magnetic field and the current enclosed by an imaginary path.

D) The magnetic field and the number of magnetic field lines.

Correct Answer: C

Content point 2 states that 'Ampère’s law relates the magnitude of the magnetic field to the current enclosed by a closed imaginary path called an Amperian loop.'

In the context of Ampère's law, what is the function of an Amperian loop?

A) It is a physical wire that carries the current being measured.

B) It is a closed imaginary path used for the integral calculation to find the enclosed current.

C) It represents the actual path of a moving charge carrier.

D) It is a device used to measure the strength of a magnetic field directly.

Correct Answer: B

Content point 2 defines an Amperian loop as a 'closed imaginary path' and it is used in the integral equation $\oint\vec{B}\cdot d\vec{l}=\mu_{0}I_{enc}$ to relate the magnetic field to the enclosed current.

For a long, straight wire carrying a current I, the magnetic field B at a distance r is given by $B=\frac{\mu_{0}I}{2\pi r}$. If the distance r from the wire is doubled, what happens to the magnitude of the magnetic field?

A) It is quadrupled.

B) It is doubled.

C) It is halved.

D) It remains unchanged.

Correct Answer: C

The equation $B=\frac{\mu_{0}I}{2\pi r}$ shows that the magnetic field B is inversely proportional to the distance r. Therefore, if r is doubled, B will be halved.

The magnetic field inside a long solenoid is described by the equation $B=\mu_{0}nI$. Based on this equation, the magnetic field strength does NOT depend on which of the following factors?

A) The current (I) flowing through the solenoid's wire.

B) The number of turns per unit length (n) of the solenoid.

C) The permeability of free space (μ₀).

D) The radius of the solenoid.

Correct Answer: D

The derived equation for the magnetic field inside a long solenoid is $B=\mu_{0}nI$. The variables are the permeability of free space (μ₀), the number of turns per unit length (n), and the current (I). The radius of the solenoid does not appear in this equation, indicating the field inside a long solenoid is uniform and does not depend on the radius.

A student is using Ampère's law in its integral form, $\oint\vec{B}\cdot d\vec{l}=\mu_{0}I_{enc}$. What does the term $I_{enc}$ specifically represent?

A) The total current that exists everywhere in the system.

B) The current that is flowing along the Amperian loop itself.

C) The current that passes through the area defined by the Amperian loop.

D) The current induced by a change in the magnetic field.

Correct Answer: C

Content point 2 states that Ampère’s law relates the magnetic field to the 'current enclosed by a closed imaginary path'. Therefore, $I_{enc}$ is the net current that pierces the surface bounded by the Amperian loop.

Ampère's law is a key component of a larger, comprehensive collection of equations that fully describe electromagnetism. What is this collection of equations called?

A) The Laws of Thermodynamics

B) Newton's Laws of Motion

C) The Ideal Gas Laws

D) Maxwell's Equations

Correct Answer: D

Content point 5 explicitly states that 'Maxwell’s equations are the collection of equations that fully describe electromagnetism' and that Ampère’s law is the basis for the fourth of these equations.

How does the spatial dependence of the magnetic field inside a long solenoid compare to that around a long, straight wire?

A) Both fields are uniform and do not depend on distance.

B) The solenoid field is uniform inside, while the wire's field strength decreases with distance from the wire.

C) The solenoid field strength decreases with distance from the center, while the wire's field is uniform.

D) Both fields decrease in strength as the inverse square of the distance.

Correct Answer: B

The equation for a solenoid, $B=\mu_{0}nI$, shows no dependence on radial position inside the solenoid, implying it is uniform. The equation for a wire, $B=\frac{\mu_{0}I}{2\pi r}$, shows the field strength decreases with distance r from the wire.

The magnetic field inside a long solenoid with n turns per unit length and current I is B. If a new solenoid is constructed with 2n turns per unit length and a current of I/2 is passed through it, what will be the new magnetic field, B'?

A) B' = B/4

B) B' = B/2

C) B' = B

D) B' = 2B

Correct Answer: C

The original field is $B=\mu_{0}nI$. The new field is $B'=\mu_{0}(2n)(I/2)$. The factors of 2 and 1/2 cancel out, so $B'=\mu_{0}nI$, which is equal to the original field B.

A long, straight wire carrying current I produces a magnetic field of magnitude B at a distance r. To produce a magnetic field of magnitude 2B at a distance of r/2 from the wire, what new current I' is required?

A) I' = I/2

B) I' = I

C) I' = 2I

D) I' = 4I

Correct Answer: B

The relationship is $B=\frac{\mu_{0}I}{2\pi r}$. We want the new field $B' = 2B$ at the new distance $r' = r/2$. So, $B' = \frac{\mu_{0}I'}{2\pi r'} = \frac{\mu_{0}I'}{2\pi (r/2)} = \frac{\mu_{0}I'}{\pi r}$. We set this equal to 2B: $\frac{\mu_{0}I'}{\pi r} = 2(\frac{\mu_{0}I}{2\pi r}) = \frac{\mu_{0}I}{\pi r}$. Comparing the two sides, we see that I' must be equal to I.

Which of the following physical situations is most appropriately analyzed using the derived equation $B=\mu_{0}nI$?

A) The magnetic field at a point very far from any current source.

B) The magnetic field near the center of a long, tightly wound coil of wire carrying a current.

C) The magnetic field a short distance from a single, long, straight current-carrying wire.

D) The magnetic field created by a single moving electron.

Correct Answer: B

Content point 4 states that Ampère’s law can be used to determine the magnetic field inside of a long solenoid, and provides the derived equation $B=\mu_{0}nI$. A long, tightly wound coil of wire is a solenoid.

What is the fundamental source of the magnetic fields described by Ampère's law in the provided content?

A) A moving charge carrier.

B) A stationary electric charge.

C) A permanent magnet.

D) A changing electric field.

Correct Answer: A

Content point 1 states that Ampère's law is used 'to describe the magnetic field created by a moving charge carrier.' A current, which is central to all the equations provided, is a flow of moving charge carriers.