Physics: Electric Forces and Coulomb's Law Worksheet

Question 1

Two small spheres have charges of +4.0 microcoulombs and -2.0 microcoulombs. State whether the electric force between them is attractive or repulsive and explain why.

Accepted Answer

The force is attractive because the two charges have opposite signs. A positive charge and a negative charge pull toward each other.

Question 2

A +2.0 x 10^-6 C charge and a +3.0 x 10^-6 C charge are separated by 0.50 m. Calculate the magnitude of the electric force between them.

Accepted Answer

The force is F = (8.99 x 10^9)(2.0 x 10^-6)(3.0 x 10^-6)/(0.50)^2 = 0.216 N. The force is repulsive because both charges are positive.

Question 3

Two charges exert a force of 12 N on each other. If the distance between the charges is doubled while the charges stay the same, what is the new force?

Accepted Answer

The new force is 3 N. Doubling the distance makes the force one-fourth as large because Coulomb's law follows an inverse-square relationship.

Question 4

A +4.0 x 10^-6 C charge and a -1.0 x 10^-6 C charge are 0.20 m apart. Calculate the magnitude and direction type of the force between them.

Accepted Answer

The force is F = (8.99 x 10^9)(4.0 x 10^-6)(1.0 x 10^-6)/(0.20)^2 = 0.899 N. The force is attractive because the charges have opposite signs.

Question 5

In one trial, charge q1 is tripled and the distance between the charges is doubled. Charge q2 stays the same. How does the new electric force compare with the original force?

Accepted Answer

The new force is three-fourths of the original force. Tripling one charge multiplies the force by 3, and doubling the distance divides the force by 4, so the factor is 3/4.

Question 6

Two charges of +5.0 x 10^-6 C and +2.0 x 10^-6 C repel each other with a force of 1.2 N. How far apart are they?

Accepted Answer

The distance is r = sqrt(k|q1q2|/F) = sqrt((8.99 x 10^9)(5.0 x 10^-6)(2.0 x 10^-6)/1.2) = 0.274 m. The charges are about 0.27 m apart.

Question 7

Three charges lie on a straight line. A +3.0 x 10^-6 C charge is 0.30 m to the left of a +2.0 x 10^-6 C charge. A -4.0 x 10^-6 C charge is 0.50 m to the right of the +2.0 x 10^-6 C charge. Find the net force on the +2.0 x 10^-6 C charge.

Accepted Answer

The left charge repels the middle charge to the right with F = 0.599 N. The right charge attracts the middle charge to the right with F = 0.288 N. The net force is 0.887 N to the right.

Question 8

A point charge of +6.0 x 10^-6 C creates an electric field. What is the magnitude of the electric field 0.20 m from the charge?

Accepted Answer

The electric field is E = k|q|/r^2 = (8.99 x 10^9)(6.0 x 10^-6)/(0.20)^2 = 1.35 x 10^6 N/C. The field points away from the positive charge.

Question 9

A -2.0 x 10^-6 C charge is placed in a uniform electric field of 500 N/C directed east. Find the magnitude and direction of the electric force on the charge.

Accepted Answer

The force magnitude is F = |q|E = (2.0 x 10^-6)(500) = 1.0 x 10^-3 N. Because the charge is negative, the force is directed west, opposite the electric field.

Question 10

Two equal positive charges are fixed on the x-axis at x = 0 m and x = 0.40 m. What is the net electric field at the midpoint between them? Explain your reasoning.

Accepted Answer

The net electric field at the midpoint is 0 N/C. The two equal positive charges create fields of equal magnitude at the midpoint, but the fields point in opposite directions and cancel.

Question 11

What are the SI units of the constant k in Coulomb's law, and why are those units needed?

Accepted Answer

The SI units of k are N m^2/C^2. These units make Coulomb's law produce a force measured in newtons when charges are in coulombs and distance is in meters.

Question 12

An object has a net charge of -3.20 x 10^-19 C. How many excess electrons does it have?

Accepted Answer

The object has 2 excess electrons. Each electron has charge -1.60 x 10^-19 C, so (-3.20 x 10^-19 C)/(-1.60 x 10^-19 C) = 2.

Question 13

A small charge A exerts an electric force of 0.75 N to the right on charge B. According to Newton's third law, what force does charge B exert on charge A?

Accepted Answer

Charge B exerts a force of 0.75 N to the left on charge A. Electric forces between two charges are equal in magnitude and opposite in direction.

Question 14

For a pair of fixed charges, the electric force is 3.6 N when the separation is 0.10 m. What is the force when the separation is 0.20 m? What is the force when the separation is 0.30 m?

Accepted Answer

At 0.20 m, the distance is doubled, so the force is 3.6/4 = 0.90 N. At 0.30 m, the distance is tripled, so the force is 3.6/9 = 0.40 N.

Question 15

A +3.0 x 10^-6 C charge attracts another charge with a force of 0.45 N when the charges are 0.30 m apart. Find the magnitude and sign of the other charge.

Accepted Answer

The magnitude is |q2| = Fr^2/(k|q1|) = (0.45)(0.30)^2/((8.99 x 10^9)(3.0 x 10^-6)) = 1.5 x 10^-6 C. The other charge is negative because it attracts the positive charge, so q2 = -1.5 x 10^-6 C.

Physics: Electric Forces and Coulomb's Law

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