Q1. A particle with charge C travels in a circular orbit with radius 4.68 mm due to the force exerted on it by a magnetic field with magnitude 1.65 T and perpendicular to the orbit.

Background

Topic: Motion of Charged Particles in Magnetic Fields

This question tests your understanding of how a charged particle moves in a magnetic field, specifically how to calculate linear and angular momentum when the particle is in circular motion due to the Lorentz force.

Key Terms and Formulas

• Linear momentum:

• Angular momentum:

• Magnetic force: (for perpendicular motion)

• Centripetal force:

Step-by-Step Guidance

1. Set the magnetic force equal to the centripetal force:

2. Solve for the velocity of the particle:

3. Use the velocity to find the linear momentum:

4. Use the velocity and radius to find the angular momentum:

Try solving on your own before revealing the answer!

Q2. Two long, parallel wires are separated by a distance of 0.400 m. The currents and have the directions shown. (a) Calculate the magnitude of the force exerted by each wire on a 1.20-m length of the other. Is the force attractive or repulsive? (b) Each current is doubled, so that $I_1$ becomes 10.0 A and $I_2$ becomes 4.00 A. Now what is the magnitude of the force that each wire exerts on a 1.20-m length of the other?

Background

Topic: Magnetic Forces Between Parallel Currents

This question tests your ability to use Ampère's law and the formula for the force between two parallel current-carrying wires.

Key Terms and Formulas

• Force per unit length between two wires:

• Total force:

• T·m/A

Step-by-Step Guidance

1. Identify the known values: A, A, m, m.

2. Write the formula for the force:

3. Plug in the values for the first scenario.

4. For the second scenario, double the currents and repeat the calculation.

Try solving on your own before revealing the answer!

Q3. An electromagnet produces a magnetic field with magnitude in a cylindrical region with a radius of between its poles. A straight wire carrying a current passes through the center of this region and is perpendicular to both the axis of the cylindrical region and the magnetic field. (a) What is the force on the wire?

Background

Topic: Magnetic Force on a Current-Carrying Wire

This question tests your understanding of the force experienced by a wire carrying current in a magnetic field, specifically when the wire is perpendicular to the field.

Key Terms and Formulas

• Magnetic force:

• For perpendicular orientation:

Step-by-Step Guidance

1. Identify the known values: , (diameter of the region), .

2. Write the formula for the force:

3. Plug in the values for , , and .

Try solving on your own before revealing the answer!