Magnetic Fields: Exploring Forces on Moving Charges and Current-Carrying Wires

What Are Magnetic Fields?

A magnetic field is a region where magnetic forces act on moving charges or magnetic materials.

Key Concepts in Magnetic Fields

Magnetic Force on a Moving Charge

A charge \([q]\) moving in a magnetic field \([B]\) experiences a force:
\[
\mathbf{F} = qvB \sin\theta
\]
Where:

• \(\mathbf{F}\): Force (N).
• \(q\): Charge (C).
• \(v\): Velocity (m/s).
• \(\theta\): Angle between \(\mathbf{v}\) and \(\mathbf{B}\).

Magnetic Force on a Current-Carrying Wire

A wire with current \([I]\) in a magnetic field experiences a force:
\[
F = BIL \sin\theta
\]
Where:

• \(L\): Length of the wire (m).

Applications of Magnetic Fields

Motors and Generators

Convert electrical energy to mechanical energy and vice versa.

Magnetic Resonance Imaging (MRI)

Uses strong magnetic fields to create detailed images of the human body.

Particle Accelerators

Guide charged particles in circular paths.

Example Problem

A \(1 \, \text{m}\) wire carries a current of \(5 \, \text{A}\) in a \(0.2 \, \text{T}\) magnetic field at \(90^\circ\). Find the force on the wire.

1. 1. Formula:

\[
F = BIL \sin\theta
\]

1. 1. Substitute Values:

\[
F = (0.2)(5)(1)\sin 90^\circ = 1 \, \text{N}
\]

Common Mistakes

1. Forgetting \(\sin\theta\).
2. Confusing \([F = qvB \sin\theta]\) and \([F = BIL \sin\theta]\).
3. Ignoring the right-hand rule for direction.

Practice Questions

1. Calculate the force on a \(2 \, \text{m}\) wire carrying \(10 \, \text{A}\) in a \(0.5 \, \text{T}\) field at \(60^\circ\).
2. Explain how motors use magnetic fields.
3. Describe an application of magnetic force on charges.