A 20-cm-radius ball is uniformly charged to 80 nC. How much charge is enclosed by spheres of radii 5, 10, and 20 cm?

"(II) Suppose the thick spherical shell of Problem 29 is a conductor. It carries a total net charge Q and at its center there is a point charge +q. What total charge is found on the outer surface of the shell?"

(II) Suppose the thick spherical shell of Problem 29 is a conductor. It carries a total net charge Q and at its center there is a point charge +q. What total charge is found on the inner surface of the shell?

An infinite cylinder of radius R has a linear charge density λ . The volume charge density (C/m³) within the cylinder (r ≤ R ) is p (r) = rp₀ / R, where p₀ is a constant to be determined. The charge within a small volume dV is dq = pdV. The integral of pdV over a cylinder of length L is the total charge Q = λL within the cylinder. Use this fact to show that p₀ = 3λ / 2πR² Hint: Let dV be a cylindrical shell of length L, radius r, and thickness dr. What is the volume of such a shell?

A rod of length $L$ lies along the $y$-axis with its center at the origin. The rod has a nonuniform linear charge density $\lambda =a\mid y\mid$, where a is a constant with the units C/m². Draw a graph of $\lambda$ versus $y$ over the length of the rod.

A proton orbits a long charged wire, making $1.0\times {10}^6$ revolutions per second. The radius of the orbit is $1.0$ cm. What is the wire's linear charge density?

CALC A 12-cm-long thin rod has the nonuniform charge density $\lambda \left(x\right)=\left(2.0\text{nC/cm}\right)e^{-\mid x\mid /\left(6.0\text{cm}\right)}$, where x is measured from the center of the rod. What is the total charge on the rod? Hint: This exercise requires an integration. Think about how to handle the absolute value sign.

A rod of length $L$ lies along the $y$-axis with its center at the origin. The rod has a nonuniform linear charge density $λ=a|y|$, where a is a constant with the units C/m². Determine the constant a in terms of $L$ and the rod's total charge $Q$.

A thin rod of length L and total charge Q has the nonuniform linear charge distribution $\lambda \left(x\right)={\lambda }_{0}x/L$, where x is measured from the rod's left end. What is ${\lambda }_0$ in terms of Q and L?