Q: Three point charges are located at the corners of an equilateral triangle as shown in the diagram. What is the magnitude of the net force on the 2.00 μC charge at the origin due to the other two charges? (Assume $$k = 8.99 \times 10^9$ N·m²/C² and all sides are 0.500 m.)

$$F = \sqrt{\left(8.99 \times 10^9$ \times \frac{2.00 \times 10$$^{-6}$$ \times 7.00 \times 10$$^{-6}$$}{(0.5)^2$}\$$right)^2$$ + \left(8.99 \times 10^9$ \times \frac{2.00 \times 10$$^{-6}$$ \times (-4.00 \times 10$$^{-6}$$)}{(0.5)^2$}\$$right)^2$$} N$$

Q: What is the value of the electric field at Point A (halfway between two positive charges of 6.00 μC and 1.50 μC, separated by 3.00 cm and 2.00 cm from a -2.00 μC charge)?

$$E = k \left( \frac{6.00 \times 10$$^{-6}$$}{0.03^2$} + \frac{1.50 \times 10$$^{-6}$$}{0.02^2$} - \frac{2.00 \times 10$$^{-6}$$}{0.05^2$} \right)$$

Q: An electric dipole is placed in an external electric field $$\vec{E}. $$What is the net torque on the dipole?

$$\vec{\tau} = \vec{p} \times \vec{E}$$

Q: A block of mass $$m$$ and charge $$Q is $$placed on a frictionless inclined plane of angle $$\theta. An $$electric field $$E is $$applied parallel to the incline. What is the expression for the magnitude of the electric field that enables the block to remain at rest?

$$E = \frac{mg}{Q} \sin \theta$$

Question 1

Three point charges are located at the corners of an equilateral triangle as shown in the diagram. What is the magnitude of the net force on the 2.00 μC charge at the origin due to the other two charges? (Assume $$k = 8.99 	imes 10^9$ N·m²/C² and all sides are 0.500 m.)

Accepted Answer

$$F = \sqrt{\left(8.99 	imes 10^9$ 	imes \frac{2.00 	imes 10$$^{-6}$$ 	imes 7.00 	imes 10$$^{-6}$$}{(0.5)^2$}\$$right)^2$$ + \left(8.99 	imes 10^9$ 	imes \frac{2.00 	imes 10$$^{-6}$$ 	imes (-4.00 	imes 10$$^{-6}$$)}{(0.5)^2$}\$$right)^2$$} N$$

Question 2

What happens to the force between two point charges if you double the charge of one of them?

Accepted Answer

It increases by a factor of 2.

Question 3

What happens to the force between two point charges if you halve the distance between them?

Accepted Answer

It increases by a factor of 4.

Question 4

Which equation correctly defines the electric field created by a point charge $$Q at a $$distance $$r$$?

Accepted Answer

$$E = \frac{kQ}{r^2$}$$

Question 5

A test charge $$q is $$placed at a distance $$d$$ from a charge $$Q. $$What is the electric field at the location of $$q$$?

Accepted Answer

$$E = \frac{kQ}{d^2$}$$

Question 6

If the test charge $$q is $$moved to half the distance from $$Q$$, what happens to the electric field at its location?

Accepted Answer

It increases by a factor of 4.

Question 7

Which principle allows you to calculate the electric field for a set of point charges?

Accepted Answer

Superposition principle

Question 8

What is the value of the electric field at Point A (halfway between two positive charges of 6.00 μC and 1.50 μC, separated by 3.00 cm and 2.00 cm from a -2.00 μC charge)?

Accepted Answer

$$E = k \left( \frac{6.00 	imes 10$$^{-6}$$}{0.03^2$} + \frac{1.50 	imes 10$$^{-6}$$}{0.02^2$} - \frac{2.00 	imes 10$$^{-6}$$}{0.05^2$} ight)$$

Question 9

Which statement about the electric field is correct?

Accepted Answer

The electric field is independent of the test charge $$q.$$

Question 10

For a point perpendicular to an electric dipole (where $$|y| \gg d$$), what is the approximate electric field?

Accepted Answer

$$E = -\frac{k p}{y^3$} \hat{x}$$

Question 11

What is the dipole moment for two charges $$+q$$ and $$-q$$ separated by a distance $$d$$?

Accepted Answer

$$p = qd$$

Question 12

An electric dipole is placed in an external electric field $$\vec{E}. $$What is the net torque on the dipole?

Accepted Answer

$$\vec{	au} = \vec{p} 	imes \vec{E}$$

Question 13

For a continuous charge distribution, which equation gives the electric field at a point?

Accepted Answer

$$E = \int k dq / r^2$ \hat{r}$$

Question 14

A long straight wire has a uniform line charge density $$\lambda. $$What is the electric field a distance $$y$$ from the wire?

Accepted Answer

$$E = \frac{2k\lambda}{y}$$

Question 15

Which direction will a positive charge move in a uniform electric field pointing upwards?

Accepted Answer

Upwards.

Question 16

Which direction will a negative charge move in a uniform electric field pointing upwards?

Accepted Answer

Downwards.

Question 17

A block of mass $$m$$ and charge $$Q is $$placed on a frictionless inclined plane of angle $$	heta. An $$electric field $$E is $$applied parallel to the incline. What is the expression for the magnitude of the electric field that enables the block to remain at rest?

Accepted Answer

$$E = \frac{mg}{Q} \sin 	heta$$

Question 18

If the block on the inclined plane had a negative charge, in which direction should the electric field be applied to keep it at rest?

Accepted Answer

Parallel to the incline, pointing down.

Question 19

Which statement best describes a conductor?

Accepted Answer

Charges can move freely through the material.

Question 20

Which statement best describes an insulator?

Accepted Answer

Charges are bound to neutral molecules and excess charge stays where it was added.

Electric Charge, Force, and Field: Study Notes

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