For the bar magnet geometry shown, d=10 units and half-length l=10 units. If percentage uncertainty in d is 1%, the percentage uncertainty in magnetic field at point P is:

Question

G1 Physics · Accepted Answer

From the source geometry, B∝(l²+d²)^(-3/2). Thus |dB/B|=[3d²/(l²+d²)]|dd/d|. With l=d=10, the factor is 3/2. Therefore percentage uncertainty in B=(3/2)(1%)=1.5%.