Question

A 20 -turn rectangular coil with sides l=20 cm and w=10 cm is placed in the y−z plane as shown in the figure. (a) If the coil, which carries a current I=20A, is in the presence of a magnetic flux density B=2×10−2(x^1+y^​3)(T), determine the maximum torque acting on the coil. (b) Find the angle ϕ for which the torque is maximum. (c) Find angle ϕ for which the torque becomes zero. Answers: (a) T=x^ +y^​ +z^ N.m (b) ϕT=max​= (c) ϕT=0​=

Answer 1

(a) To determine the maximum torque acting on the coil, we can use the formula:


`T = N * B * A * sin(ϕ)`

Given:
N = 20 turns
B = 2×10^−2(x^1+y^3) T
A = l * w = (20 cm) * (10 cm) = 200 cm^2 = 0.02 m^2
I = 20 A

To find the maximum torque, we need to find the angle ϕ that maximizes the sine function. Since the maximum value of the sine function is 1, the maximum torque occurs when sin(ϕ) = 1.

Substituting the given values into the torque formula, we have:

T = 20 * (2×10^−2(x^1+y^3)) * 0.02 * 1
T = 0.008(x^1+y^3) N.m

(b) To find the angle ϕ for which the torque is maximum, we substitute sin(ϕ) = 1 into the torque formula:

T = N * B * A * sin(ϕ)
0.008(x^1+y^3) = 20 * (2×10^−2(x^1+y^3)) * 0.02 * 1

Simplifying the equation, we find:
0.008 = 0.008

This equation is true for all values of ϕ. Therefore, the angle ϕ for which the torque is maximum can be any value.

(c) To find the angle ϕ for which the torque becomes zero, we need to find the value of ϕ that makes sin(ϕ) = 0. The sine function is zero at ϕ = 0, ϕ = π, ϕ = 2π, etc.

Therefore, the angle ϕ for which the torque becomes zero can be any multiple of π.

(a) T = 0.008(x^1+y^3) N.m
(b) ϕT=max = Any value
(c) ϕT=0 = Any multiple of π.