(b) electric field strength E = Q / (4πε₀r²) for a point charge

The idea

The electric field strength E at a distance r from a point charge Q is the force per unit positive charge placed at that point. For a point charge in a vacuum or air, E = Q / (4πε₀r²). The field is radial: it points away from a positive charge and towards a negative charge. The magnitude follows an inverse-square law, so doubling r reduces E to one quarter. For example, a point charge of +4.0 × 10⁻⁹ C produces a field of about 4.0 × 10² N C⁻¹ at 0.30 m. The equation applies to point charges and outside spherically symmetric charge distributions; inside a uniform spherical shell the field is zero.

What earns the marks

• Defines electric field strength as force per unit positive charge.
• Uses the equation E = Q / (4πε₀r²) for a point charge.
• Recognises that E is a vector directed radially away from positive charge and towards negative charge.
• Applies the inverse-square dependence on distance r.
• States that the equation is valid for point charges or outside spherically symmetric distributions.

Common mistakes and how to put them right

• Confusing electric field strength with electric potential.

  Put it right: Field strength is a vector with units N C⁻¹, while potential is a scalar with units V.

• Using the test charge q in the numerator instead of the source charge Q.

  Put it right: The field of a point charge depends only on the source charge and the distance.

• Forgetting to square the distance.

  Put it right: E is proportional to 1/r², not 1/r.

Exam tips

• State the direction of E relative to the sign of the source charge before calculating its magnitude.
• Convert all distances to metres and charges to coulombs before substituting into the equation.
• In multiple-choice questions, check that the units of the options are N C⁻¹ and that the distance dependence is inverse-square.