Two similar magnetic poles, having pole strengths in the ration 1:3 and placed 1m apart. Find the point where a unit pole experiences no net force due to these two poles

Explanation

Let the pole strenght of the two magnetic poles be m and 3 m . Suppose the required point is located at distance x from the first pole . Then at this point

Force on unit pole due to first pole = Force on unit pole due to second pole
or `" " (mu_(0))/(4 pi) . (m xx 1)/(x^(2)) = (mu_(0))/(4pi) . (3mxx1)/((1-x)^(2))`
or `" " 3 x^(2) = (1-x)^(2) "or" sqrt3 x = 1-x `
or `" " x = (1)/(1 + sqrt3) = 0.366` m