Question

A particle is shot at a velocity of 3 × 10⁴ m/s to the right and enters the magnetic field generated by a large, flat current-carrying sheet. The current in the sheet is parallel to the particle’s initial line of motion. The particle exits the magnetic field 6.8 cm directly above the location where it enters.

(a) Is the particle’s charge positive or negative?
(b) If the sheet carries a current of 4 A/m, what is the ratio of the charge on the particle to its mass?

Answer

Part (a) – Determining the Sign of the Charge

Since the particle enters the magnetic field and exits directly above the entry point, it has been deflected upward. If its velocity is to the right and the current in the sheet is also to the right, then:

• The magnetic field (B) is directed into the page above the sheet (by right-hand rule).
• For a positive charge, using the right-hand rule with v to the right and B into the page, the force would be downward.
• However, the particle is deflected upward, so it must be a negative charge.

Part (b) – Ratio of Charge to Mass (q/m)

The magnetic force provides the centripetal force that causes circular motion:

Magnetic field due to current-carrying sheet:

For a current density I = 4 A/m, and μ₀ = 4π × 10⁻⁷ T·m/A, and considering r = 0.068 m, we substitute:

Substituting the values:

Simplifying: