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Magnetic Fields and Charges

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Magnetic Fields and Charges

Use conventional current and the right-hand rule for positive charges. In diagrams, ⊙ means out of the page and ⊗ means into the page. Show working for calculations, include units, and state directions clearly.

Field directions and particle paths

A research team is checking how charged particles behave in a uniform magnetic field.

A. Positive charge: v →, B ↑. Force direction?

B. Negative charge: v ↑, B ⊗. Force direction?

C. Positive charge: v parallel to B. Force direction and magnitude?

D. Negative charge is stationary in a magnetic field. Force direction and magnitude?

1.For case A in the direction key, use the right-hand rule to explain why the force points that way.

2.For case B, determine the force direction. Show the positive-charge result first, then explain how the negative charge changes it.

3.Which statement best describes the magnetic force on a moving charge?

It is always parallel to the magnetic field.
It is perpendicular to both velocity and magnetic field, when it is non-zero.
It always changes the particle’s speed.
It acts on stationary charges whenever a field is present.

4.A proton travels at 2.0 × 10⁶ m s⁻¹ through a 0.30 T magnetic field. Its velocity is at 30° to the field. Calculate the magnetic force magnitude. Use q = 1.60 × 10⁻¹⁹ C.

5.A particle moves through a magnetic field and follows a curved path. Explain why the magnetic force changes its direction but not its kinetic energy.

Using a magnetic field to steer particles

A positively charged particle enters a uniform field at right angles to the field. The magnetic force provides the centripetal force, producing circular motion.

6.Starting with magnetic force F = qvB for perpendicular motion and centripetal force F = mv²/r, equate the forces and rearrange to make r the subject.

7.A singly charged positive ion has mass 3.2 × 10⁻²⁷ kg and speed 4.0 × 10⁵ m s⁻¹. It enters a perpendicular 0.20 T field. Calculate the radius of its path. Use q = 1.60 × 10⁻¹⁹ C.

8.The ion in question 7 enters the same field at the same speed, but the magnetic-field strength is doubled. What happens to its path radius? Explain using the radius relationship.

9.A student says, “If a charged particle moves parallel to a magnetic field, it will curve because magnetic fields always exert a force.” Identify the error and give the correct force for this situation.