Q: Two positive charges $$Q = 3.5\ \mu\mathrm{C}$$ are placed $$10\ \mathrm{cm}$$ apart. What is the magnitude of the electric field at point A, which is $$5\ \mathrm{cm}$$ from the right charge and $$10\ \mathrm{cm}$$ from the left charge?

$$E = 6.3 \times 10^5$\ \mathrm{N/C}$$

Question 1

At each corner of a square of side $$l = 20\ \mathrm{cm}$$ there are point charges of magnitude $$Q$$, $$2Q$$, $$3Q$$, and $$4Q$$ where $$Q = 3\ \mu\mathrm{C}. $$What is the magnitude of the net force on the charge $$3Q$$ due to the other three charges?

Accepted Answer

$$F = 3.24\ \mathrm{N}$$

Question 2

In the square charge configuration from Question 1, what is the direction of the net force on the $$3Q$$ charge?

Accepted Answer

Along the diagonal away from the $$Q$$ charge

Question 3

Two positive charges $$Q = 3.5\ \mu\mathrm{C}$$ are placed $$10\ \mathrm{cm}$$ apart. What is the magnitude of the electric field at point A, which is $$5\ \mathrm{cm}$$ from the right charge and $$10\ \mathrm{cm}$$ from the left charge?

Accepted Answer

$$E = 6.3 	imes 10^5$\ \mathrm{N/C}$$

Question 4

For the same two-charge setup, what is the direction of the electric field at point B, which is $$5\ \mathrm{cm}$$ from the left charge and $$10\ \mathrm{cm}$$ from the right charge?

Accepted Answer

To the right

Question 5

Three charges $$-Q$$, $$+Q$$, and $$-3Q$$ are placed at the vertices of an equilateral triangle of side $$3\ \mathrm{cm}. $$What is the electric potential at the midpoint of side AB?

Accepted Answer

$$V = \dfrac{1}{4\pi\$$epsilon_0$$} \left( \dfrac{-Q}{1.5\ \mathrm{cm}} + \dfrac{+Q}{1.5\ \mathrm{cm}} + \dfrac{-3Q}{d} \right)$$

Question 6

You build a parallel plate capacitor using two aluminum disks of diameter $$20\ \mathrm{cm}$$ separated by $$2.5\ \mathrm{cm}. $$What is the capacitance of this capacitor?

Accepted Answer

$$C = \$$epsilon_0$$ \dfrac{A}{d}$$, where $$A = \pi r^2$ and r = 10$$\ \mathrm{cm}$$

Question 7

If the capacitor from the previous question is connected to a $$9\ \mathrm{V}$$ battery, what is the charge stored on each disk?

Accepted Answer

$$Q = C 	imes V$$

Question 8

What is the electric field between the plates of the capacitor connected to a $$9\ \mathrm{V}$$ battery?

Accepted Answer

$$E = \dfrac{V}{d}$$

Question 9

What is the work done by the battery to charge the capacitor to voltage $$V$$?

Accepted Answer

$$W = \dfrac{1}{2} C V^2$

Question 10

If you insert a dielectric with $$K = 3.75$$ between the plates of the capacitor, what happens to the capacitance?

Accepted Answer

It increases by a factor of $$K$$

Question 11

You want to design a portable heating pad that runs on a $$3.0\ \mathrm{V}$$ battery. If you use a $$1.0\ \mathrm{mm}$$ diameter aluminum wire as the heating element, how long should the wire be to generate $$12\ \mathrm{W} of $$heating power?

Accepted Answer

$$L = \dfrac{\rho A}{R}$$, where $$R = \dfrac{V^2$}{P}$$

Question 12

If you connect the same heating pad to a $$12\ \mathrm{V}$$ battery instead of $$3.0\ \mathrm{V}$$, what happens to the power generated?

Accepted Answer

It increases by a factor of $$16$$

Question 13

If you connect the heating pad designed for $$3.0\ \mathrm{V} to a$$ $$12\ \mathrm{V}$$ battery, what is a likely consequence?

Accepted Answer

The wire will overheat and may melt

Question 14

A capacitor is charged to $$9\ \mathrm{V}$$ and then disconnected from the battery. If a dielectric is inserted, what happens to the voltage across the plates?

Accepted Answer

It decreases by a factor of $$K$$

Question 15

In the equilateral triangle charge configuration, what is the direction of the electric field at the midpoint of side BC?

Accepted Answer

Towards vertex A

Question 16

If you double the separation between the plates of a parallel plate capacitor, what happens to its capacitance?

Accepted Answer

It is halved

Question 17

A $$3.5\ \mu\mathrm{C}$$ charge is placed $$5\ \mathrm{cm}$$ from another identical charge. What is the magnitude of the force between them?

Accepted Answer

$$F = \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{Q^2$}{r^2$}$$

Question 18

If you add a sheet of paper (dielectric constant $$K = 3.75) $$between the plates of a capacitor connected to a battery, what happens to the charge stored on the plates?

Accepted Answer

It increases by a factor of $$K$$

Electrostatics and Electric Fields: Study Notes and Problem Analysis

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