Force directions and core ideas

• Magnetic force on a moving charge: $F = qvB\sin\theta$.

• Magnetic force is maximum when $v \perp B$ and zero when $v \parallel B$.

• Magnetic force is always perpendicular to the particle’s velocity, so it changes direction only, not speed or kinetic energy.

• Electric force on a charge: $F = qE$.

• Electric force acts in the direction of the field for a positive charge and opposite the field for a negative charge.

• For direction questions, use the right-hand rule for a positive charge/current; reverse the direction for a negative charge.

• In exam answers, state clearly whether the field causes a change in speed, direction, or both.

Motion in a uniform electric field

• A charged particle in a uniform electric field experiences a constant force: $F = qE$.

• So the particle has constant acceleration: $a = \frac{qE}{m}$.

• If the particle enters parallel to the field, it speeds up or slows down in a straight line.

• If it enters perpendicular to the field, the motion is projectile-like: constant velocity in one direction and constant acceleration in the field direction.

• A positive charge curves with the field; a negative charge curves against the field.

• Common exam method: resolve motion into independent perpendicular components.

• Link to energy when needed: work done by the field changes the particle’s kinetic energy.

This diagram shows the uniform electric field between parallel plates and the relation $E = V/d$. It is useful for visualising why a charged particle in this region experiences a constant force. The curved field lines at the edges also help explain why most exam questions assume the particle stays in the uniform central region. Source

Motion in a uniform magnetic field

• A moving charge in a uniform magnetic field experiences a force only if it has velocity component perpendicular to the field.

• If $v \perp B$, the magnetic force provides the centripetal force.

• Therefore: $qvB = \frac{mv^2}{r}$, so $r = \frac{mv}{qB}$.

• A larger mass or speed gives a larger radius; a larger charge magnitude or magnetic field strength gives a smaller radius.

• The particle moves in a circle when the velocity is fully perpendicular to the field.

• If the velocity has both parallel and perpendicular components, the path is helical.

• Kinetic energy stays constant in a magnetic field because the magnetic force does no work.

• Required practical/exam idea: determine charge-to-mass ratio from the measured path radius in a known magnetic field.

This figure shows a charged particle moving in a circular path in a uniform magnetic field, with velocity tangent to the circle and force toward the centre. It is ideal for revising why the magnetic force acts as the centripetal force. The sign of the charge matters for the direction of curvature. Source

Perpendicular electric and magnetic fields

• In crossed fields, the particle experiences both electric and magnetic forces.

• If the forces are equal and opposite, the particle passes through undeflected.

• Balance condition: $qE = qvB$, so selected speed is $v = \frac{E}{B}$.

• This is the basis of a velocity selector.

• Particles with the wrong speed are deflected because one force is larger than the other.

• Always compare the directions of the two forces before setting them equal.

• If the electric field is removed, the particle then follows the magnetic-field path only.

This figure shows electric and magnetic forces acting in opposite directions on moving charge carriers. It helps you visualise the force balance used in a velocity selector, even though the example is the Hall effect. Use it to practise deciding when a particle is undeflected because $qE = qvB$. Source

Magnetic force on a current-carrying conductor

• A current-carrying wire in a magnetic field experiences a force: $F = BIL\sin\theta$.

• Here $L$ is the length of conductor in the field, $I$ is current, and $\theta$ is the angle between the current and the field.

• The force is maximum when the conductor is perpendicular to the field and zero when parallel.

• Direction is found using the right-hand rule for conventional current.

• This is the basis of the motor effect.

• In calculations, make sure the length used is the part of the wire inside the field.

This diagram shows a wire segment between magnet poles and the resulting force on the conductor. It is useful for linking the equation $F = BIL\sin\theta$ to the physical setup. The built-in hand-rule sketch is especially helpful for direction questions. Source

Force between parallel wires

• One current-carrying wire produces a magnetic field that acts on the other wire.

• The force per unit length is $\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi r}$.

• Same current direction $\rightarrow$ attractive force.

• Opposite current directions $\rightarrow$ repulsive force.

• The force is larger for bigger currents and smaller separation.

• In explanations, say explicitly that the force exists because each wire lies in the magnetic field produced by the other.

This figure shows how one wire creates a magnetic field that exerts a force on the other wire. It clearly illustrates why parallel currents in the same direction attract. The top view is helpful for force-direction questions involving the right-hand rule. Source