# Integral of magnetic field over the sphere

1. Jan 12, 2014

### hokhani

If all the currents were inside a sphere with the radius R, then we would have $\int B \,dV= 2/3\mu_0 M$ where $M$ is magnetic moment of all the currents and $B$ is magnetic field. If all the current were outside the sphere, then we would have$\int B \,dV= 4/3 \pi R^3 B(0)$ where $B(0)$is magnetic field at center of the sphere (Both the relations above are derived in Jackson).
Now, how about the situation in which all the currents were on the surface of the sphere? Can one say that both the two relations above are hold simultaneously?

2. Jan 13, 2014

### Simon Bridge

Why not work it out and see?