AP (Advanced Placement) · AP Physics C: Electricity and Magnetism
5 multiple-choice questions marked as you go, and 2 written questions with worked solutions. All on Electric Charge and Electric Force.
Two infinite, parallel non-conducting sheets carry surface charge densities \(+\sigma\) and \(-2\sigma\) respectively. The sheets are separated by a distance \(d\). If the sheet with \(+\sigma\) is located at \(z = 0\) and the sheet with \(-2\sigma\) is at \(z = d\), determine the electric field vector in the region \(0 < z < d\).
Consider an infinite non-conducting sheet with a uniform surface charge density \(\sigma\). A small circular hole of radius \(R\) is cut out of the sheet. Find the magnitude of the electric field at a point \(P\) located at a distance \(z\) directly above the center of the hole.
A non-conducting sphere of radius \(R\) carries a non-uniform volume charge density given by \(\rho(r) = \rho_0 \frac{r}{R}\) for \(r \le R\), and \(0\) otherwise. Using Gauss's Law, find the magnitude of the electric field at a distance \(r < R\) from the center.
A thin spherical shell of radius \(R\) has a total charge \(Q\) distributed uniformly over its surface. A point charge \(q\) is placed at a distance \(r = R/2\) from the center. What is the magnitude of the electrostatic force acting on the point charge \(q\)?
A point charge \(+q\) is located at the center of a cube of side length \(L\). What is the electric flux through one of the faces of the cube?
A non-conducting solid sphere of radius \(R\) has a non-uniform volume charge density given by \(\rho(r) = \rho_0 \frac{r}{R}\), where \(r\) is the distance from the center. Using Gauss's Law, find the expression for the electric field strength \(E\) at a point inside the sphere where \(r < R\).
Write your answer out first, then check it against the worked solution.
A solid non-conducting sphere of radius \(R\) carries a non-uniform volume charge density given by \(\rho(r) = \rho_0 (1 - \frac{r}{R})\) for \(r \le R\), and \(\rho = 0\) for \(r > R\), where \(\rho_0\) is a positive constant.
(a) Use Gauss's Law to derive an expression for the electric field magnitude \(E\) as a function of distance \(r\) from the center for \(r \le R\).
(b) Determine the value of \(r\) at which the electric field intensity is maximum.
Write your answer out first, then check it against the worked solution.
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