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Q3. (a) A formula associated with the magnetic field strength of a solenoid is given by:

B = (μ₀ N r² I)/(2(r²+x² )^3/2

Calculate the value of x when B = 0.01, μ₀ = 4π × 10^-7, N = 1000, r = 0.1 and I = 10. (8)

(b) Solve the following system of equations for A and B in the range of

0 ≤ A ≤ π/2 and 0 ≤ B ≤ π/2 radians.

3sin A + 4cos B = 1.77

2sin A – cos B = 0.52 (8)