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

Magnitude: $$E = 1.26 \times 10^6$\ \mathrm{N/C}$$, direction: to the right

Q: Three point 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?

$$V = -\dfrac{Q}{4\pi\$$epsilon_0$$ \times 1.5\ \mathrm{cm}}$$

Q: You build a parallel plate capacitor using two aluminum disks of radius $$10\ \mathrm{cm}$$ separated by $$2.5\ \mathrm{cm}. $$What is the capacitance of this capacitor?

$$C = 1.11 \times 10$$^{-10}$$\ \mathrm{F}$$

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

$$Q = 1.00 \times 10$$^{-9}$$\ \mathrm{C}$$

Q: How much work is done by the battery to charge the capacitor to $$9\ \mathrm{V}$$?

$$W = 4.5 \times 10$$^{-9}$$\ \mathrm{J}$$

Q: If you insert a sheet of paper with dielectric constant $$K = 3.75$$ between the plates of the capacitor, what is the new capacitance?

$$C = 4.16 \times 10$$^{-10}$$\ \mathrm{F}$$

Q: If the heating pad wire is $$1.0\ \mathrm{mm} in $$diameter and $$0.76\ \mathrm{m}$$ long, what is its resistance? (Resistivity of aluminum $$\rho = 2.82 \times 10$$^{-8}$$\ \Omega\cdot\mathrm{m})$$

$$R = 2.72 \times 10$$^{-1}$$\ \Omega$$

Q: What is the energy stored in the capacitor when connected to a $$9\ \mathrm{V}$$ battery and filled with paper ($$K = 3.75$$)?

$$U = 1.68 \times 10$$^{-8}$$\ \mathrm{J}$$

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 acting on the charge $$3Q$$ due to the other three charges?

Accepted Answer

$$F = 3.67\ \mathrm{N}$$

Question 2

Two positive charges $$Q = 3.5\ \mu\mathrm{C}$$ are placed $$10\ \mathrm{cm}$$ apart. What is the magnitude and direction 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

Magnitude: $$E = 1.26 	imes 10^6$\ \mathrm{N/C}$$, direction: to the right

Question 3

Three point 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

$$V = -\dfrac{Q}{4\pi\$$epsilon_0$$ 	imes 1.5\ \mathrm{cm}}$$

Question 4

You build a parallel plate capacitor using two aluminum disks of radius $$10\ \mathrm{cm}$$ separated by $$2.5\ \mathrm{cm}. $$What is the capacitance of this capacitor?

Accepted Answer

$$C = 1.11 	imes 10$$^{-10}$$\ \mathrm{F}$$

Question 5

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

$$Q = 1.00 	imes 10$$^{-9}$$\ \mathrm{C}$$

Question 6

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

Accepted Answer

$$E = 360\ \mathrm{V/m}$$

Question 7

How much work is done by the battery to charge the capacitor to $$9\ \mathrm{V}$$?

Accepted Answer

$$W = 4.5 	imes 10$$^{-9}$$\ \mathrm{J}$$

Question 8

If you insert a sheet of paper with dielectric constant $$K = 3.75$$ between the plates of the capacitor, what is the new capacitance?

Accepted Answer

$$C = 4.16 	imes 10$$^{-10}$$\ \mathrm{F}$$

Question 9

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

$$L = 0.76\ \mathrm{m}$$

Question 10

If you connect the same heating pad to a $$12\ \mathrm{V}$$ battery, what will happen to the power generated?

Accepted Answer

The power will increase by a factor of $$16$$

Question 11

A $$3.0\ \mathrm{V}$$ battery is used to power a heating pad made of aluminum wire. If the resistance of the wire is $$0.75\ \Omega$$, what is the current through the wire?

Accepted Answer

$$I = 4.0\ \mathrm{A}$$

Question 12

If the heating pad wire is $$1.0\ \mathrm{mm} in $$diameter and $$0.76\ \mathrm{m}$$ long, what is its resistance? (Resistivity of aluminum $$ho = 2.82 	imes 10$$^{-8}$$\ \Omega\cdot\mathrm{m})$$

Accepted Answer

$$R = 2.72 	imes 10$$^{-1}$$\ \Omega$$

Question 13

What is the energy stored in the capacitor when connected to a $$9\ \mathrm{V}$$ battery and filled with paper ($$K = 3.75$$)?

Accepted Answer

$$U = 1.68 	imes 10$$^{-8}$$\ \mathrm{J}$$

Question 14

If the distance between the plates of the capacitor is doubled, what happens to the capacitance?

Accepted Answer

It is halved

Question 15

A $$9\ \mathrm{V}$$ battery is used to charge a capacitor. If the battery is disconnected after charging, what happens to the charge on the plates?

Accepted Answer

The charge remains the same

Question 16

If you replace the aluminum disks in the capacitor with copper disks of the same size, what happens to the capacitance?

Accepted Answer

It remains the same

Question 17

In the triangle with charges $$-Q$$, $$+Q$$, and $$-3Q$$, what is the direction of the electric field at the midpoint of side BC?

Accepted Answer

Toward vertex A

Question 18

If the heating pad wire is replaced with a wire of half the diameter, what happens to the resistance?

Accepted Answer

It increases by a factor of 4

Electrostatics and Electric Fields: Problem Set Study Guide

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