Question

Two charges -q and q are placed on a line at x = -d and x = d respectively. What is a fourth order approximation to the electric potential v (x) for |x| < d?

Answer 1

The fourth-order approximation to the electric potential v(x) for |x| < d can be found using a Taylor series expansion.

Step-by-step explanation:

To find the fourth-order approximation to the electric potential v(x) for |x| < d, we can use a Taylor series expansion. The electric potential can be expressed as a function of the distance from the charges, x, using the formula:

v(x) = kq(1/d) + kq(x^2/(2d^3)) - kq(x^4/(8d^5))

where k is the Coulomb constant and q is the magnitude of the charge. This expression gives us an approximation of the electric potential v(x) for |x| < d, up to the fourth order term.