8. A proton enters a uniform magnetic field at a speed v. The magnetic field is oriented at an angle ϕ to the direction of the proton, and the strength of the field is B. Which change or set of changes would double the magnitude of the force on the proton? (1 point)\

The force on the proton doubles if

- The speed of the proton is doubled.

- The strength of the magnetic field in which it is moving is doubled.

- If the proton moves with angle θ to the field, such that (sin θ = 2 sin ϕ). As long as ϕ ≤ 30°, a corresponding θ can be found that will satisfy the condition (sin θ = 2 sin ϕ) and double the magnitude of the force on the proton.

Explanation:

Force on a charge q moving with velocity v in a magnetic field of strength B at angle ϕ is given by

F = qvB sin ϕ

To double the magnitude of the force on the proton, any of the other parameters can be tweaked (apart from the charge on the proton) to double the force on the proton.

The force on the proton doubles if

- The speed of the proton is doubled.

- The strength of the magnetic field in which it is moving is doubled.

- If the proton moves with angle θ to the field, such that (sin θ = 2 sin ϕ). As long as ϕ ≤ 30°, a corresponding θ can be found that will satisfy the condition (sin θ = 2 sin ϕ) and double the magnitude of the force on the proton.

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explanation:

two charges are fixed in place on the x-axis as shown. the charge at x = 0 is negative and has magnitude q = 2 μcoulombs (1 μcoulomb = 10-6 coulombs). the charge at x = d, (d = +12 cm), is positive and has magnitude q = 4 μcoulombs. find a point x = xo along the x-axis at which the electric field is zero.