A charged particle is moving horizontally westward with a velocity of 3.5 × 10⁶ m/s in a region where there is a magnetic field of magnitude 5.6 × 10^-5 T directed vertically downward. The particle experiences a force of 7.8 × 10^-16 N northward. What is the charge on the particle?

Question

Quizplus · Accepted Answer

The force on a charged particle moving in a magnetic field is given by the equation F = qvB sin(θ), where q is the charge on the particle, v is its velocity, B is the magnitude of the magnetic field, and θ is the angle between the velocity and the magnetic field. In this case, the force is northward, so θ must be 90 degrees (or pi/2 radians). We can solve for q using the given values:
F = qvB sin(θ)
7.8 × 10^-16 N = q(3.5 × 10^16 m/s)(5.6 × 10^-5 T)(1)   (since sin(90) = 1)
q = (7.8 × 10^-16 N) / (3.92 × 10^-4 C)
q = -1.99 × 10^-12 C, which can be expressed in scientific notation as -1.99 × 10^-12 C = -1.99 × 10^-9 μC = -1.99 nC. Therefore, the closest answer choice is B, -4.0 × 10^-18 C, which is approximately twice the value we calculated. None of the other answer choices are even close, so B is the best choice.

A Charged Particle Is Moving Horizontally Westward with a Velocity