Question

A charge feels a 2.89 x 10^-7 N force when it moves 288 m/s perpendicular (90°) to the magnetic field of 2.77 x 10^-5 T. How big is the charge?

Answer 1

To find the charge magnitude, we use the formula F = qvBsin(θ), and since the charge moves perpendicularly to the magnetic field, sin(θ) equals to 1, simplifying the formula to q = F / (vB). After substituting the given values into the simplified formula, we can calculate the charge.

Step-by-step explanation:

The student is asking about the calculation of charge value given the magnetic force, velocity, and magnetic field strength. According to the equation F = qvBsin(θ), where F is the magnetic force, q is the charge magnitude, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field, we can solve for the charge q since the angle θ is given as 90° (perpendicular movement), making sin(θ) equal to 1.

Thus, the equation becomes F = qvB. Rearranging the formula to solve for q gives us q = F / (vB). Plugging in the given values, we get q = (2.89 x 10^-7 N) / (288 m/s * 2.77 x 10^-5 T), which after calculation provides the magnitude of the charge.

Answer 2

To find the magnitude of the charge, we can use the formula for the magnetic force on a moving charge: F = qvBsin(θ). Plugging in the given values, the charge is 1.046 x 10^-5 C.

Step-by-step explanation:

To find the magnitude of the charge, we can use the formula for the magnetic force on a moving charge:

F = qvBsin(θ)

where F is the magnetic force, q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field.

In this case, we are given the force, velocity, and magnetic field strength, so we can rearrange the formula to solve for the charge:

q = F / (vBsin(θ))

Plugging in the given values:

q = (2.89 x 10^-7 N) / (288 m/s * 2.77 x 10^-5 T * sin(90°))

q = 1.046 x 10^-5 C