Quiz: Moving Charges and Magnetism — 9 questions

1. A charged particle moves at an angle of $90^\circ$ to a uniform magnetic field. Which expression gives the magnetic force on the particle?

A. $F=qB\sin v$

B. $F=\frac{qv}{B}$

C. $F=qvB$

D. $F=\frac{mv^2}{qB}$

Answer: (C)

Explanation

At $90^\circ$, $\sin\theta=1$, so the general relation $F=qvB\sin\theta$ becomes $F=qvB$. A velocity parallel to the field would instead make the force zero because the sine factor would vanish.

2. A charged particle moves through a uniform magnetic field with its velocity perpendicular to the field. Which equation describes the role of the magnetic force in its circular motion?

A. $qvB=\frac{m}{vr}$

B. $qvB=\frac{mv}{r^2}$

C. $qvB=mr^2$

D. $qvB=\frac{mv^2}{r}$

Answer: (D)

Explanation

For perpendicular motion in a uniform magnetic field, the magnetic force provides the centripetal force, giving $qvB=\frac{mv^2}{r}$. The other expressions do not represent the centripetal-force balance for circular motion.

3. A straight current-carrying conductor lies at an angle of $90^\circ$ to a magnetic field. What is the magnitude of the force on the conductor?

A. $F=Il/B$

B. $F=Bl/I$

C. $F=BI/l$

D. $F=BIl$

Answer: (D)

Explanation

The conductor-force relation is $F=BIl\sin\theta$, and at $90^\circ$ the sine factor equals one, producing $F=BIl$. If the conductor were parallel to the field, the force would be zero rather than maximum.

4. Two parallel conductors carry currents in the same direction. How do the magnetic forces between them compare?

A. They rotate into perpendicular directions.

B. They exert no force on each other.

C. They attract each other.

D. They repel each other.

Answer: (C)

Explanation

Parallel currents flowing in the same direction attract one another. Oppositely directed parallel currents repel, so current direction determines the interaction.

5. What is the primary physical quantity that determines the magnitude of the force on a straight current-carrying conductor in a magnetic field?

A. The magnetic field strength, the current, and the length of the conductor, as well as the angle between the current and the magnetic field.

B. The current and the distance between the conductor and the magnetic source.

C. The magnetic field strength and the length of the conductor, regardless of the current.

D. Only the magnetic field strength and the current in the conductor.

Answer: (A)

Explanation

The force on a straight current-carrying conductor depends on the magnetic field strength, the current, the length of the conductor, and the angle between the current and the magnetic field. The formula $F=BIl extsin\theta$ captures this relationship, unlike options that omit some of these factors.

6. What is the formula for the magnetic field at the center of a circular loop with N turns and radius R?

A. $B=\frac{\mu_0 I}{2 \pi R}$

B. $B=\frac{\mu_0 N I}{R}$

C. $B=\frac{\mu_0 N I}{4 \pi R}$

D. $B=\frac{\mu_0 N I}{2 R}$

Answer: (D)

Explanation

The magnetic field at the center of a circular loop with N turns and radius R is given by $B=\frac{\mu_0 N I}{2 R}$. The other options either omit the number of turns or have incorrect coefficients.

7. What is the primary purpose of a galvanometer in electrical measurements?

A. To detect and measure small electric currents

B. To convert electrical energy into mechanical energy

C. To amplify electrical signals for transmission

D. To store electrical energy temporarily

Answer: (A)

Explanation

A galvanometer is primarily used to detect and measure small electric currents by observing the deflection of a needle. It is not designed for energy conversion, amplification, or storage.

8. How does the magnetic force on a charged particle differ when its velocity is parallel versus perpendicular to a uniform magnetic field?

A. The magnetic force is the same in both cases, always causing the particle to accelerate.

B. When the velocity is parallel, the magnetic force is zero; when perpendicular, it is maximum and causes circular motion.

C. When the velocity is parallel, the magnetic force causes circular motion; when perpendicular, the force is zero.

D. When the velocity is perpendicular, the force is zero; when parallel, it causes the particle to spiral.

Answer: (B)

Explanation

The magnetic force on a charged particle is $F=qvB\text{sin}\theta$, so it is zero when the velocity is parallel to the magnetic field (θ=0°), and maximum when perpendicular (θ=90°), resulting in circular motion.

9. What causes the magnetic force on a charged particle to result in circular motion when moving in a uniform magnetic field?

A. The magnetic force supplies the centripetal force needed for circular motion.

B. The magnetic force opposes the particle's velocity, causing it to spiral.

C. The magnetic force aligns the particle's velocity with the magnetic field.

D. The magnetic force causes the particle to accelerate linearly along the field.

Answer: (A)

Explanation

The magnetic force acts perpendicular to the particle's velocity, providing the centripetal force necessary for circular motion. If the force were not perpendicular, the particle would not follow a circular path.