A short magnetic dipole of moment M is placed at the origin with its magnetic moment along the x-axis. Point P has coordinates (a,a), where a is much larger than the size of the magnet. The magnetic field magnitude at P is:
Options

Question

A short magnetic dipole of moment M is placed at the origin with its magnetic moment along the x-axis. Point P has coordinates (a,a), where a is much larger than the size of the magnet. The magnetic field magnitude at P is:

Options

G1 Physics · Accepted Answer

For a short magnetic dipole, B = (μ₀M/4πr³)√(1+3cos²θ). For P(a,a), r = √(a²+a²) = a√2, and the position vector makes angle θ = 45° with the x-axis. Hence, cos²θ = 1/2. Therefore, B = μ₀M/[4π(a√2)³] · √(1+3/2) = μ₀M/[4π(2a²)^(3/2)] · √(5/2). Hence option A is correct.