4. (10 points) (a)A 2.4 cm diameter, 16 cm long solenoid is tightly wound with o

Question

4. (10 points) (a)A 2.4 cm diameter, 16 cm long solenoid is tightly wound with one layer of 1.0 mm diameter wire. A 2.0 A current runs In the wire. What is the magnitude of the magnetic field Inside the solenoid? (b) A square coil of wire is 4.0 cm on a side and has 50 turns. The loop is in a 1.3 T uniform magnetic field. The current In the coil is 3.0 A. The axis of the coil, perpendicular to the plane of the coil, Is 30 from the field direction. What is the magnitude of the torque on the coil?

Explanation / Answer

Here ,

a)

L is the length

N is the number of turns

I is the current

as the magnetic field of solenoid is given as

B = u0*N*I/L

B = 4pi *10^-7 * 2 *(0.16/.001) * 2/0.16

B = 0.00503 T

the magnetic field inside solenoid is 0.00503 T

b)

here,

as magnetic torque = u * B * sin(theta)

theta is angle between magnetic moment and magnetic field

magnetic torque = N * A * I * B * sin(30)

magnetic torque = 0.04^2 * 50 * 3 * 1.3 * sin(30)

magnetic torque = 0.156 N.m

the magnitude of magnetic torque is 0.156 N.m

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