Test on Lorentz force and particle motion in a magnetic field

Question 1: Increasing the magnitude of a charged particle's charge in a uniform magnetic field causes it to follow a wider circular path.

A. Yes

B. No

Explanation: According to the radius formula (r = m · v / (|q| · B)), a larger magnitude of charge (|q|) will result in a smaller radius of curvature. This means the particle follows a tighter circular path, not a wider one.

Question 2: When a charged particle moves perpendicular to a uniform magnetic field, increasing its initial speed will cause it to follow a wider circular path.

A. Yes

B. No

Explanation: The study materials explain that increasing the initial speed (v) of the particle leads to a larger radius of curvature. The radius formula (r = m · v / (|q| · B)) directly shows that 'r' is proportional to 'v', meaning a higher 'v' results in a larger 'r', causing the particle to move in a wider circle.

Question 3: A positively charged particle moves with a velocity perpendicular to a uniform magnetic field, resulting in a circular path. Based on the provided study materials, which of the following statements correctly describes how changes to the particle's initial conditions or the magnetic field would affect its motion?

A. If the magnitude of the particle's charge were increased, the particle would follow a larger circular path.

B. If the particle's initial speed were increased, its period of revolution would increase.

C. If the strength of the magnetic field were increased, the particle would complete a revolution more quickly.

D. If the particle's initial velocity had a component parallel to the magnetic field, it would still follow a purely circular path, but with a different radius.

Explanation: The radius of the circular path is given by r = m · v / (|q| · B). The period of revolution is given by T = 2πm / (|q| · B). Option 0 is incorrect: According to the formula, if the magnitude of the charge (|q|) were increased, the radius (r) would decrease, resulting in a tighter, smaller circular path. Option 1 is incorrect: The study materials state that the period of the circular motion (T = 2πm / (|q| · B)) is independent of the particle's speed (v). Option 2 is correct: If the strength of the magnetic field (B) were increased, the period (T) would decrease, meaning the particle would complete its revolution more quickly. Option 3 is incorrect: The study materials explicitly state that if the particle's initial velocity has a component parallel to the magnetic field, the particle will move in a helical (spiral) path, not a purely circular path.

Question 4: According to the study materials, which of the following statements about the period of a charged particle's circular motion in a uniform magnetic field are correct?

A. The period of the circular motion is directly proportional to the particle's speed.

B. The period of the circular motion is independent of the particle's speed.

C. The period of the circular motion is directly proportional to the magnetic field strength.

D. The period of the circular motion is inversely proportional to the magnitude of the particle's charge.

Explanation: The study materials explicitly state: "The period of the circular motion is independent of the particle's speed and the radius of its path." This makes option 1 incorrect and option 2 correct. The formula for the period is T = 2πm / (|q| · B). This shows that the period (T) is inversely proportional to the magnitude of the charge (|q|) and the magnetic field strength (B). Therefore, option 3 is incorrect because the period is inversely proportional to the magnetic field strength, not directly proportional. Option 4 is correct because T is inversely proportional to |q|.

Question 5: Charged particles from the solar wind are repelled by Earth's magnetic field.

A. Yes

B. No

Explanation: Charged particles from the solar wind are trapped by Earth's magnetic field, not repelled by it. The Lorentz force guides these particles along the magnetic field lines.