Topic 4.2: Electric and Magnetic Fields Questions

Two identical point charges, a fixed distance apart, exert a force F on each other.

One of the charges is then replaced by a charge half as large, with the separation unchanged.

State the new force on each charge, in terms of F.

State what is meant by the electric field strength at a point.

State the shape of the magnetic field lines around a long straight current-carrying wire.

Two parallel metal plates are connected to a battery so that the upper plate is positive and the lower plate is negative.

State what is meant by a uniform electric field, and state the direction of the field between the plates.

Outline how charging by contact differs from charging by induction, including the sign of the final charge in each case relative to the charged object first brought up.

A positively charged rod is brought close to, but not touching, an isolated neutral metal sphere.

While the rod is held in place the sphere is briefly earthed and the earth connection is then removed; finally the rod is taken away.

A small test charge of 1.5 × 10⁻⁹ C is placed at a point in an electric field and experiences a force of 3.6 × 10⁻⁵ N.

Calculate the electric field strength at that point.

Two long parallel plates are held a few centimetres apart, the left plate positive and the right plate negative.

Sketch the pattern of the electric field lines in the gap between the plates, and explain one feature of your sketch that shows the field is uniform.

Two point charges, q₁ = 3.0 × 10⁻⁶ C and q₂ = 4.0 × 10⁻⁶ C, are 0.25 m apart.

Small oil drops are sprayed into the top of a vertical tube and fall through it.

As a drop passes through the spray nozzle it picks up charge by friction.

Two long parallel wires are 0.15 m apart and carry currents of 8.0 A and 12 A in the same direction.

Calculate the force per unit length on each wire, state whether the wires attract or repel, and explain how the force on the 8.0 A wire compares with the force on the 12 A wire.

(μ₀ = 4π × 10⁻⁷ T m A⁻¹.)

A long straight vertical wire carries a steady current upwards.

Using the right-hand grip rule, describe the direction of the magnetic field at a point directly to the EAST of the wire.

Two small charged spheres, q₁ = 5.0 × 10⁻⁶ C and q₂ = 8.0 × 10⁻⁶ C, are held 0.40 m apart.

A plastic rod is rubbed with a dry cloth and becomes negatively charged.

Two small positive point charges lie on a straight horizontal line in a vacuum. A charge of +3.0 μC is fixed at point X, and a charge of +6.0 μC is fixed at point Y, with X and Y separated by 0.30 m. Point P lies on the line between the charges, 0.10 m from X (and therefore 0.20 m from Y).

Using k = 9.0 × 10⁹ N m² C⁻², what is the magnitude of the resultant electric field strength at P?

A proton (charge +1.6 × 10⁻¹⁹ C) starts from rest at one plate and is accelerated through a potential difference of 1.8 kV to the other plate.

An ion of charge +2e (where e = 1.6 × 10⁻¹⁹ C) is released from rest at the positive plate and accelerated across two parallel plates with a potential difference of 350 V.

Two long parallel wires are 0.080 m apart.

They carry currents of 6.0 A and 9.0 A in opposite directions.

Determine the force per unit length on each wire and state whether the wires attract or repel.

(μ₀ = 4π × 10⁻⁷ T m A⁻¹.)

In the theory of electromagnetism, the speed of light in a vacuum c is related to the permeability of free space μ₀ and the permittivity of free space ε₀ by c = 1/√(μ₀ε₀).

What is the product μ₀ε₀ expressed in fundamental SI units?

Two small spheres carry charges of q₁ = −6.0 × 10⁻⁶ C and q₂ = +9.0 × 10⁻⁶ C and are held 0.50 m apart.

Calculate the magnitude of the electric force between them and state whether it is attractive or repulsive.

(k = 8.99 × 10⁹ N m² C⁻².)