Question 3: (7 points).
Consider a point charge q=10?? C.
a) What is the flux ? passing through a spherical shell of radius R=10 cm with the point charge at its
center?
b) What is the flux ? passing through a spherical shell of Radius R=1 m with the point charge at its
center?
Hint: For the simple charge, the electric field is in the radial direction \hat{r}, which is exactly the same as the
normal to the surface (the spherical shell) \hat{n}. Also, the electric field is constant on the shell (since the
shell represents a constant value of r=R, R is a constant). The electric field of a simple charge at distance
r from the charge : $E(r) = \frac{kq}{r^2} \hat{r}$.
Given:
- $\oint_{S} \text{flux } \Phi = \oint_{\text{(shell of radius R)}} E(R) \cdot d\vec{A}$
- $\oint_{\text{(shell of radius R)}} d\vec{A}$ for a spherical shell of radius R = area of spherical shell = $4\pi R^2$
Bonus part. 2 points.
Assume now that that point charge is surrounded by a cubic shell as shown, with the charge at its
center.
What is the flux ? passing through the cubic shell? (Hint: The flux represents the number of field lines
passing through a surface, think about that!)
