Section 5.2: Magnetic Forces
Magnetic forces act on moving charges or currents in a magnetic field. The force depends on the charge, velocity, and magnetic field direction.
- Force on a Moving Charge: \[ \mathbf{F} = q \mathbf{v} \times \mathbf{B} \] where \( q \) = charge, \( \mathbf{v} \) = velocity, \( \mathbf{B} \) = magnetic field.
- Force on a Current-Carrying Wire: \[ \mathbf{F} = I \mathbf{L} \times \mathbf{B} \] where \( I \) = current, \( \mathbf{L} \) = length vector in the direction of current.
- Direction of force is determined using the **right-hand rule**.
- Magnitude of force on a charge: \( F = qvB\sin\theta \), where \( \theta \) is the angle between velocity and magnetic field.
Example: Force on a Moving Charge
A proton moves at \(2 \times 10^6 \, \text{m/s}\) perpendicular to a 0.5 T magnetic field. Find the force on the proton.
\[ F = qvB = (1.6 \times 10^{-19})(2 \times 10^6)(0.5) = 1.6 \times 10^{-13} \, \text{N} \]
Practice Problems
- Calculate the force on an electron moving at \(10^6 \, \text{m/s}\) at 30° to a 0.2 T magnetic field.
- A wire 0.5 m long carries 3 A current perpendicular to a 0.1 T field. Find the force on the wire.
- Explain how the right-hand rule is used to determine the direction of magnetic force on a moving charge.
- Describe the effect on the force if the velocity of the charge is parallel to the magnetic field.
- Two wires carrying currents in opposite directions are placed close to each other in a magnetic field. Describe the forces acting on each wire.