In a magnetic field, field lines are curves to which the magnetic field B is everywhere tangential. By evaluating dBJds, where s is the distance measured along a field line, prove that the radius of curvature at any point on a field line is given by B3 |B × (B · ỹ)B[' with B denoting the magnitude of the magnetic field and |.| stands for the magnitude of the vector.

In a magnetic field, field lines are curves to which the magnetic field B is everywhere tangential. By evaluating dBJds, where s is the distance measured along a field line, prove that the radius of curvature at any point on a field line is given by B3 |B × (B · ỹ)B[' with B denoting the magnitude of the magnetic field and |.| stands for the magnitude of the vector.