A rectangular coil with a length of 6.0 cm and a width of 4.0 cm and 250 turns is placed in a uniform magnetic field with a magnitude of 0.88 T. (a) If the maximum torque experienced by the coil is 0.13 N · m, determine the current in the coil.

0.246 A.

Explanation:

Current: This can be defined as the rate of flow of charge in an electric Circuit. The S. I unit of current is Ampere (A).

The expression containing torque, magnetic Field, Current, Area and Number of turns is given as,

τ = BANI ... Equation 1

Where τ = Torque, B = Magnetic Field, A = Area, N = Number of Turns, I = current in the coil.

Make I the subject of the equation.

I = τ/BAN ... Equation 2

Given: τ = 0.13 N. m, B = 0.88 T, N = 250 Turns

But, A = Length (L) * Width (W) = LW

Where L = 4.0 cm = 0.04 m, W = 6.0 cm = 0.06 m

A = 0.04*0.06 = 0.0024 m²

Substitute into equation 2

I = 0.13 / (0.88*250*0.0024)

I = 0.13/0.528

I = 0.246 A.

Answer: 0.246 A

Explanation: The relationship between the torque experienced by a rectangular current carrying loop, it area and number of turns is given as

T = NAIB cosθ

Where T = torque, A = Area, B = strength of magnetic field, I = Current, N = number of turns

The torque will be maximum when θ is 90°

Hence Tmax = NAIB

N = 250, B = 0.88T

A = length * breadth = 0.04 * 0.06 = 0.0024 m², Tmax = 0.13 Nm

0.13 = 250 * 0.0024 * 0.88 * I

0.13 = 0.528 * I

I = 0.13 / 0.528 = 0.246 A