Free Coulomb's Law MCQs with Answers

1. According to Coulomb's law, the force between two point charges is proportional to

• A. the product of the charges and inversely proportional to the distance between them
• B. the product of the charges and inversely proportional to the square of the distance
• C. the sum of the charges and the square of the distance
• D. the square of the product of the charges

Explanation: The inverse square dependence means doubling the separation quarters the force, exactly as in Newton's law of gravitation. The difference is that charges may repel as well as attract, and the electrostatic force between two protons is some 10 to the 36 times stronger than their gravitational attraction. Both laws describe point objects, or spheres treated as points at their centres.

2. If the distance between two point charges is halved, the electrostatic force between them becomes

• A. half
• B. double
• C. four times
• D. one quarter

Explanation: Force varies as one over the square of the separation, so halving the distance multiplies the force by four. Answering double treats the relationship as a simple inverse, which is the standard error. Tripling the distance would reduce the force to one ninth by the same reasoning.

3. The force between two charges placed in a medium of relative permittivity 4, compared with the force in a vacuum, is

• A. four times greater
• B. one quarter
• C. unchanged
• D. twice as great

Explanation: The medium appears in the denominator of Coulomb's law, so a relative permittivity of 4 reduces the force to a quarter of its vacuum value. Water has a relative permittivity of about 80, which is why ionic compounds dissociate so readily in it: the attraction between the ions is weakened eightyfold. Air is close enough to 1 that the vacuum formula is normally used for it.

4. If a plastic sheet of relative permittivity 2.5 is inserted between two point charges placed in vacuum, then the electrostatic force between them

• A. Increases by a factor of 2.5
• B. Decreases by a factor of 2.5
• C. Increases by a factor of 5
• D. Decreases by a factor of 5

Explanation: Relative permittivity appears in the denominator of Coulomb's law, so inserting a medium of relative permittivity 2.5 reduces the force to 1 over 2.5 of its vacuum value. Water, with a relative permittivity of about 80, weakens ionic attraction eightyfold, which is why ionic compounds dissociate so readily in it. Air is close enough to 1 that the vacuum formula is used for it.

5. If the distance between two charges is halved and magnitude of charges are also doubled, then the force between these charges becomes:

• A. Two times
• B. Four times
• C. Eight times
• D. Sixteen times

Explanation: Doubling both charges multiplies the numerator of Coulomb's law by four, and halving the separation divides the denominator by four since the distance is squared, so the two effects combine to give sixteen times the original force. Handling the two changes separately and then multiplying is the safe method. Forgetting that the distance is squared gives the eight times answer.