Question

A conducting cylinder of radius $r_1$ and length l is nested inside a cylindrical shell with the same length and radius $r_2$. The inside and outside of this cylindrical capacitor is connected to the terminals of a battery of voltage, $V$. The charge density on the inner cylinder is $+$.
Which one of the following statements is FALSE?

• A. The electric field has constant magnitude at all points between the cylinders.
• B. The capacitance depends directly on the length, ll, of the cylinders.
• C. If $r_2$ remains fixed and $r_1$ becomes smaller, the capacitance will decrease.
• D. The outer cylinder has a smaller surface charge density than the inner cylinder.
• E. Filling the space between the cylinders with an insulating plastic will increase the capacitance.

Answer 1

Answer: (A)

The electric field has constant magnitude at all points between the cylinders.

The capacitance of a cylindrical capacitance=$\frac{2\pi K{ϵ}_{0}l}{ln\left(\frac{r_2}{r_1}\right)}$

Hence options B,C,D,E are true.

However the electric field is not constant at all points between the cylinders.