A 0.780 m long section of cable carrying current to a car starter motor makes an angle of 60.0° with the Earth's 5.50 ✕ 10-5 T field. What is the current (in A) when the wire experiences a force of 7.00 ✕ 10-3 N?

188 A

Explanation:

Parameters given:

Length of cable, L = 0.78 m

Angle, θ = 60º

Magnetic field, B = 5.5 * 10^ (-5) T

Force experienced by wire, F = 7 * 10^ (-3) N

The force experienced by a current carrying wire of length L, due to a magnetic field B is given as:

F = I * L * B * sinθ

=> I = F / (L * B * sinθ)

I = (7 * 10^ (-3)) / (0.78 * 5.5 * 10^ (-5) * sin60)

I = 188 A

The current is 188.17Amperes

Explanation:

The formula for calculating the force carrying current on a conductor placed in a magnetic field is expressed as shown;

F = BILsin (theta) where;

F is the force on the conductor = 7.00 ✕ 10^-3 N

B is the earth's magnetic field = 5.50 ✕ 10^-5 Tesla

I is the current = ?

L is the length of the conductor = 0.78m

theta is the angle that the conductor make with the earth's magnetic field = 60.0°

Making the current I the subject of the formula from the equation gives;

I = F/BLsin (theta)

Substituting the given data's in the formula to get current in the wire;

I = 7.00 ✕ 10^-3 / (5.50 ✕ 10^-5 * 0.78 * sin60°)

I = 7.00*10^-3/3.72*10^-5

I = 188.17Amperes