Part 1#

Write an expression in terms of $x$, $d$ and $R$ for the distance, $r_1$, for the distance of any point on ring 1 from point $P$. Note that this is a right-angled triangle so you can use the pythagorean theorem.

Use the following table as a reference for each variable:

If the answer is 0, enter “zero”.

Part 2#

Write an expression for the electric potential at point $P$ due to the two thin rings in terms of $Q$, $R$, $d$ and $x$.

Use the following table as a reference for each variable:

If the answer is 0, enter “zero”.

Part 3#

From your expression for the potential energy find the electric field at point $P$. Note that it points along the $x$-axis, and remember to use the chain rule.

Use the following table as a reference for each variable:

If the answer is 0, enter “zero”.

Part 4#

When $x=-\frac{d}{2}$ evaluate the electric potential.

Use the following table as a reference for each variable:

If the answer is 0, enter “zero”.

Part 5#

When $x=-\frac{d}{2}$ evaluate the electric field.

Use the following table as a reference for each variable:

If the answer is 0, enter “zero”.

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.