Electric fields: Electric fields

Question 1

State Coulomb’s law in words for the electrostatic force between two point charges.

Answer 1

The electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the separation between their centres.

Question 2

Write the equation for the magnitude of the electrostatic force F between charges Q1 and Q2 separated by distance r.

Answer 2

F = (1/(4πε0)) * (Q1 Q2 / r**2).

Question 3

Give the value and units of the permittivity of free space ε0.

Answer 3

ε0 = 8.854 × 10^-12 F m^-1.

Question 4

Write the expression for the magnitude of the force between a large charge Q and test charge q separated by distance r.

Answer 4

F = (1/(4πε0)) * (Q q / r**2).

Question 5

Explain how the sign of the force in Coulomb’s law indicates attraction or repulsion.

Answer 5

A positive force indicates repulsion (like charges), a negative force indicates attraction (unlike charges).

Question 6

Define an electric field.

Answer 6

A region of space in which a stationary charged particle experiences a force.

Question 7

Describe the electric field lines around an isolated positive point charge.

Answer 7

They radiate outwards from the charge to infinity, never crossing, with density decreasing with distance.

Question 8

Describe the electric field lines around an isolated negative point charge.

Answer 8

They converge towards the charge from infinity, never crossing, with density decreasing with distance.

Question 9

Describe the electric field lines between oppositely charged parallel plates.

Answer 9

They are straight, parallel and equally spaced, directed from positive to negative plate.

Question 10

Define electric field strength E at a point.

Answer 10

The force per unit (positive test) charge acting on a small stationary test charge at that point.

Question 11

Write the equation linking electric field strength E, force F and test charge q.

Answer 11

E = F / q.

Question 12

Derive the expression for the magnitude of E at distance r from a point charge Q.

Answer 12

Substitute F = (1/(4πε0)) * (Q q / r2) into E = F / q to get E = (1/(4πε0)) * (Q / r2).

Question 13

Write the formula for electric field strength E due to a point charge Q at distance r.

Answer 13

E = (1/(4πε0)) * (Q / r**2) (magnitude).

Question 14

What are the SI units of electric field strength E?

Answer 14

N C^-1 or V m^-1.

Question 15

Is electric field strength E a scalar or vector quantity?

Answer 15

It is a vector quantity; its direction is the direction of the force on a positive test charge.

Question 16

How does the magnitude of E due to a point charge vary with distance r?

Answer 16

|E| ∝ 1 / r**2 (decreases with the inverse square of distance).

Question 17

Explain qualitatively how electric field strength varies with distance from a point charge.

Answer 17

The field lines become more widely spaced further from the charge, so field strength decreases with distance.