A square frame with a side of 5 cm, with 10 turns, is in a uniform magnetic field with an induction of 0.1 T.

A square frame with a side of 5 cm, with 10 turns, is in a uniform magnetic field with an induction of 0.1 T. The plane of the frame makes an angle of 0 ° with the direction of the magnetic field. Determine the torque of the forces acting on the frame if the current in the frame is 4 A.

a = 5 cm = 0.05 m.

B = 0.1 T.

n = 10.

∠β = 0 °.

I = 4 A.

M -?

The moment of force M, which acts on the frame with a current in a magnetic field, is expressed by the formula: M = n * I * B * S * sinα, where n is the number of turns of the frame, B is the magnetic induction of the field, I is the current in the frame, S Is the area of ​​the frame, ∠α is the angle between the perpendicular to the area of ​​the frame S and the vector of magnetic induction B.

Since the plane of the frame makes an angle ∠β = 0 ° with the vector of magnetic induction B, then ∠α = 90 ° – ∠β = 90 ° – 0 ° = 90 °.

sinα = sin90 ° = 1.

Since the frame has a square shape, its area S is expressed by the formula: S = a ^ 2.

M = n * I * B * a ^ 2.

M = 10 * 4 A * 0.1 T * (0.05 m) ^ 2 = 0.01 N / m.

Answer: a moment of force M = 0.01 N / m acts on the frame with current.