Question

Consider the hemispherical closed surface in the figure below. The hemisphere is in a uniform magnetic field that makes an angle ? with the vertical.

(a) Calculate the magnetic flux (?B) through the flat surface S1. (Use any variable or symbol stated above along with the following as necessary: pie.)

?B = __________.

(b) Calculate the magnetic flux (?B) through the hemispherical surface S2. (Use any variable or symbol stated above along with the following as necessary: pie.)

?B =__________.

Answer 1

(a) \(\left(\varphi_{\mathrm{B}}\right)_{\text {flat }}=\mathrm{BA}=\mathrm{B} \pi \mathrm{R}^{2} \cos (180 \cdot \theta)=-\mathrm{B} \mathrm{nR}^{2} \cos \theta\)

(b) The net flux out of the closed surfaceis zero \(\left(\varphi_{B}\right)_{\text {flat }}+\left(\varphi_{B}\right)_{\text {curved }}=0\)

\(\left(\varphi_{\mathrm{B}}\right)_{\text {curved }}=\mathrm{B} \pi \mathrm{R}^{2} \cos \theta\)