Question

In electromagnetic theory, the magnetic potential u at a point on the axis of a circular coil is given by u=arſº sa to store u= A dx (r2 + x2)(3/2) where A, r, a are constants. Compute U = Hint: The integration is a little tricky. Substitute x = r tan 0.

Answer 1

To compute U, substitute x = r tan(θ) in the given expression and evaluate the integral.

Step-by-step explanation:

To compute U, we start by substituting x = r tan(θ) in the given expression. This gives us:

U = A ∫[0 to h] (r^2 + r^2 tan^2(θ))(3/2) r sec^2(θ) dθ

Where h is the angle such that tan(h) = ∞, and r is a constant. The integral can be solved using trigonometric identities and integration by substitution. After evaluating the integral, we get the value of U.