The force on a charge moving

with a velocity v in a magnetic
field B is half of the maximum
force when the angle between
wave B is:
A. 0°
B. 90°
C. 45°
D. 30°

1 answer

The force on a charge moving in a magnetic field is given by the equation F = qvBsinθ, where F is the force, q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field vector.

To find the angle at which the force is half of the maximum force, we can set F = (1/2)F_max and solve for θ.

(1/2)F_max = qvBsinθ

Since sinθ has a maximum value of 1, we can rewrite the equation as:

(1/2)F_max = qvB

Now we can solve for θ.

(1/2)F_max = qvB

(1/2)(qvB) = qvB

(1/2) = sinθ

sinθ = 1/2

θ = sin^(-1)(1/2)

θ = 30°

Therefore, the angle between the velocity vector and the magnetic field vector when the force is half of the maximum force is 30°.

Answer: D. 30°