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

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.