A rectangular loop of wire carrying a 4.0-A current is placed in a magnetic field of 0.60 T. The magnitude of the torque acting on this wire when the plane of the loop makes a 30° angle with the field is measured to be 1.1 N · m. What is the area of this loop?

a) 0.20 m2

b) 0.53 m2

c) 0.26 m2

d) 0.80 m2

e) 0.40 m2

option B

Explanation:

given,

rectangular loop carrying current (I) = 4 A

magnetic field (B) = 0.6 T

the magnitude of torque = 1.1 N m

angle = 30°

we know,

τ = N I A B sin θ

θ = is the angle between Area vector and magnetic field so θ = 60°

1.1 = 1 x 4 x A x 0.6 x sin 60°

1.1 = 2.078 x A

A = 0.53 m²

hence, the correct answer is option B

b) A = 0.52 m²

Explanation:

Given that

I = 4 A

B = 0.6 T

θ=90° - 30° = 60°

T = 1.1 N. m

We know that torque T given as

T = I B A sinθ

Now by putting the values

T = I B A sinθ

1.1 = 4 x 0.6 x A x sin 60°

A = 0.52 m²