Free Electrostatics 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. Electric field intensity at a point is defined as

• A. the force per unit positive charge placed at that point
• B. the work done in bringing a charge to that point
• C. the charge per unit area
• D. the potential at that point

Explanation: Field intensity is a vector measured in newtons per coulomb, equivalently volts per metre, and it points in the direction a positive test charge would be pushed. Work done per unit charge is potential, a scalar, and confusing the two is the most common error in this chapter. The test charge must be small enough not to disturb the field it is measuring.

5. The electric field intensity at a distance r from a point charge q is

• A. proportional to q and to r
• B. proportional to q and inversely proportional to r squared
• C. independent of r
• D. proportional to r squared

Explanation: Dividing the Coulomb force by the test charge leaves E equal to kq over r squared, so the field also obeys an inverse square law and points radially outwards for a positive charge. Field lines drawn from such a charge spread out into space, and their decreasing density with distance is a picture of the same falling intensity. For a uniform field, as between parallel plates, E is constant instead.

6. Electric field lines

• A. can cross one another
• B. start on negative charges and end on positive charges
• C. never cross, because the field has only one direction at each point
• D. are always straight

Explanation: Two crossing lines would mean two different field directions at the same point, which is impossible for a single resultant vector. Lines run from positive to negative charge, and their spacing represents the strength of the field. They are straight only for simple arrangements such as an isolated point charge or a uniform field.

7. Inside a hollow charged conductor in electrostatic equilibrium, the electric field is

• A. zero everywhere
• B. maximum at the centre
• C. equal to the field just outside
• D. directed towards the centre

Explanation: Charges on a conductor arrange themselves on the outer surface until the field inside cancels completely; any residual field would move the free electrons until it did. This is the basis of the Faraday cage, which is why a car is a relatively safe place in a lightning storm and why sensitive equipment is shielded in metal boxes. The field just outside the surface, by contrast, is not zero.

8. Electric potential at a point is

• A. a vector measured in newtons per coulomb
• B. the work done per unit positive charge in bringing it from infinity to that point
• C. the force per unit charge
• D. the charge stored per unit voltage

Explanation: Potential is a scalar measured in volts, so potentials from several charges are added arithmetically with their signs rather than as vectors, which makes it far easier to handle than field intensity. Force per unit charge is the field, and charge per unit voltage is capacitance. Only differences in potential have physical meaning, which is why infinity is chosen as the zero.

9. The work done in moving a charge between two points on the same equipotential surface is

• A. maximum
• B. zero
• C. negative
• D. equal to qV

Explanation: Work equals charge multiplied by the potential difference, and on an equipotential surface that difference is zero, so no work is done however long the path. It follows that field lines always meet equipotential surfaces at right angles, since any component along the surface would do work. The surface of any conductor in equilibrium is an equipotential.

10. An electron volt is the energy gained by an electron when it moves through a potential difference of

• A. one volt
• B. one joule
• C. 1000 volts
• D. one coulomb

Explanation: Since energy is charge multiplied by potential difference, one electron volt equals 1.6 times 10 to the minus 19 joules, the magnitude of the electronic charge in coulombs. The unit is convenient because joules are absurdly large for single particles. Electron volts and their multiples are the standard currency of atomic and nuclear physics.