Physics: Electric Forces and Coulomb's Law
Calculating electric forces between charged particles
Physics: Electric Forces and Coulomb's Law
Calculating electric forces between charged particles
Physics - Grade 9-12
- 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.
Like charges repel, and opposite charges attract.
The force is attractive because the two charges have opposite signs. A positive charge and a negative charge pull toward each other. - 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.
Substitute the charge values in coulombs and the distance in meters.
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. - 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?
The force is proportional to 1/r^2.
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. - 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.
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. - 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?
Track each change as a multiplier on the original force.
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. - 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?
Rearrange Coulomb's law to solve for r.
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. - 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.
Find the force from each neighboring charge on the middle charge, then add forces with direction.
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. - 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?
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. - 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.
A positive charge feels force with the field, while a negative charge feels force opposite the field.
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. - 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.
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. - 11
What are the SI units of the constant k in Coulomb's law, and why are those units needed?
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. - 12
An object has a net charge of -3.20 x 10^-19 C. How many excess electrons does it have?
Divide the total charge by the charge of one electron.
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. - 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?
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. - 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?
Compare each new distance to 0.10 m and use the inverse-square relationship.
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. - 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.
Solve Coulomb's law for the unknown charge and use attraction to determine its sign.
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.