Question

Figure (36-E1) shows some of the equipotential surfaces of the magnetic scalar potential. Find the magnetic field B at a point in the region.

Answer 1

Given:
Perpendicular distance, dx = 10 sin30^ₒ cm = 0.05 m,
Change in the potential, dV = 0.1 × 10⁻⁴ T-m
We know that the relation between the potential and the field is given by
$$\begin{gathered} B=-\frac{dV}{dx} \\ \Rightarrow B=-\frac{0.1\times {10}^{-4}\mathrm{T}-m}{5\times {10}^{-2}m} \\ \Rightarrow B=-2\times {10}^{-4}\mathrm{T} \end{gathered}$$
B is perpendicular to the equipotential surface. Here, it is at angle of 120° with the positive x-axis.