Question

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.

Answer 1

0.246 A.

Step-by-step 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 2

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