Magnetic Field — Sources, Properties & Right-Hand Rule

A magnetic field describes how magnets, moving charges, and electric currents influence other moving charges and magnetic materials in the space around them. It is written as $B$ and measured in tesla $(\mathrm{T})$.

The main idea is directional. A magnetic field is a vector field, so at each point it has both a size and a direction. The right-hand rule is the usual shortcut for finding that direction in simple cases.

What A Magnetic Field Means

You can think of a magnetic field as the part of the electromagnetic environment that tells you how a moving charge or a current-carrying wire would be pushed.

For a charge $q$ moving with speed $v$ at angle $\theta$ to the field, the magnetic-force magnitude is

$$F = qvB\sin\theta$$

This condition matters. If the charge is not moving, the magnetic part of the force is zero. If it moves exactly parallel or antiparallel to the field, then $\sin\theta = 0$ and the magnetic force is also zero.

Where Magnetic Fields Come From

In introductory physics, the most common sources are electric currents, moving charges, and permanent magnets. A coil of wire with current creates a magnetic field, and so does a bar magnet.

In full electromagnetism, a changing electric field can also produce a magnetic field. That is important in electromagnetic waves, transformers, and Maxwell's equations, but many first problems focus on currents and simple magnets.

Key Properties To Remember

Magnetic field is a vector, so direction is part of the answer, not an extra detail.

Magnetic fields add by superposition. If two sources create fields at the same point, the net field is the vector sum of those fields.

Field lines are a visual aid, not physical strings. At any point, the field direction is tangent to the field line.

In standard introductory treatment, magnetic field lines form closed loops rather than starting and ending the way electric field lines do on charges.

The Right-Hand Rule For A Straight Current

For a straight wire carrying conventional current, point your right thumb in the direction of the current. Your curled fingers show the direction of the magnetic field circling the wire.

This is one of the most useful versions of the right-hand rule because it gives direction quickly without extra algebra.

Be careful about the current definition. The rule uses conventional current, which points in the direction positive charge would move. In a metal wire, electrons drift the opposite way.

Worked Example: Field Around A Long Straight Wire

Suppose a long straight wire carries a steady current upward. You want the direction of the magnetic field at a point to the right of the wire.

Use the right-hand rule. Point your right thumb upward with the current. Your fingers curl around the wire. At the point to the right of the wire, the field points into the page.

If you also need the field strength, a common special-case formula is

$$B = \frac{\mu_0 I}{2\pi r}$$

This formula applies for a long straight wire carrying steady current, evaluated at distance $r$, in vacuum or air to a good approximation. Here $\mu_0$ is the permeability of free space.

For example, if $I = 5.0\ \mathrm{A}$ and $r = 0.020\ \mathrm{m}$, then

$$B = \frac{(4\pi \times 10^{-7})(5.0)}{2\pi(0.020)}$$ $$B = 5.0 \times 10^{-5}\ \mathrm{T}$$

So the field at that point has magnitude $5.0 \times 10^{-5}\ \mathrm{T}$ and direction into the page.

That example shows the two parts of a magnetic-field answer: magnitude from the formula, direction from the right-hand rule.

Common Mistakes

• Treating magnetic field as a scalar and giving only the size.
• Forgetting that the right-hand rule uses conventional current, not electron flow.
• Using $B = \mu_0 I / (2\pi r)$ for any shape of wire, even when the wire is not approximately long and straight.
• Assuming a magnetic field always pushes a charge. A stationary charge feels no magnetic force.
• Mixing up the direction of the field with the direction of the force on a moving charge.

Where The Concept Is Used

Magnetic fields are used in motors, generators, transformers, MRI systems, speakers, compasses, and charged-particle motion.

They also sit behind a lot of circuit and electromagnetism ideas. Once current creates a magnetic field, you can explain inductors, electromagnets, and why changing fields matter in electromagnetic induction.

Try A Similar Case

Try your own version with the same wire, but place the point to the left of the wire instead of the right. Keep the same current and distance. First use the right-hand rule to get the direction, then check whether the magnitude changes.