Magnetism

Any moving charge creates a magnetic field, which can interact with other moving charges or with magnetic materials. This is a fundamental difference from electric fields: electric fields are produced by static charges, but magnetic fields arise only when charges are in motion. Magnetic field strength is measured in tesla (T), the SI unit — a fairly large unit, so everyday magnetic fields are often reported in microtesla (µT) or millitesla (mT).

Key Takeaways

• Magnetic fields are created only by moving charges, measured in tesla (T).

• Materials are diamagnetic (weakly repelled, no residual magnetism), paramagnetic (weakly attracted, no residual magnetism), or ferromagnetic (strongly attracted, retains magnetism).

• A straight wire's field: B = μ0I/(2πr). A circular loop's center field: B = μ0I/(2r).

• Magnetic force on a moving charge: FB = qvB sin θ — maximum at 90°, zero at 0°.

• Magnetic force on a current-carrying wire: FB = ILB sin θ — same angle dependence.

• The right-hand rule finds force direction, but its application differs for a moving charge versus a current-carrying wire.

Classes of Magnetic Materials

Materials are classified into three categories based on how they respond to an external magnetic field:

• Diamagnetic materials are weakly repelled by an external field. All their electrons are paired, so their magnetic moments cancel each other out. When exposed to a field, a diamagnetic material develops a small, temporary magnetic moment in the opposite direction of the applied field — but the effect is weak and vanishes once the field is removed.

• Paramagnetic materials are weakly attracted to an external field. They contain unpaired electrons with permanent magnetic moments, but without a field these moments are randomly oriented, so the material shows no strong magnetism on its own. An external field aligns the moments slightly, producing weak attraction.

• Ferromagnetic materials show the strongest magnetic behavior. Unpaired electrons' magnetic moments align in the same direction even without an external field, producing a permanent alignment that persists after the field is removed. Iron, cobalt, and nickel are common examples — all can be magnetized into permanent magnets.

Magnetic Fields from Current-Carrying Wires

Long straight wire. A current-carrying straight wire generates a magnetic field around it. At a distance r from the wire, the field strength is:

B = μ0I/(2πr)

where B is the magnetic field strength, μ0 is the permeability of free space (4π×10⁻⁷ T·m/A), I is the current in the wire, and r is the distance from the wire. The field forms concentric circles around the wire.

MCAT Callout — Worked Example: Magnetic Field from a Straight Wire: A straight wire carries a current of 5 A. At a distance of 0.02 m from the wire:

B = (4π×10⁻⁷)(5)/(2π×0.02) = 5×10⁻⁵ T = 50 µT

Circular loop. A similar field arises when current flows through a circular loop of wire. At the center of the loop:

B = μ0I/(2r)

where r is the loop's radius and I is the current through it. The field is strongest at the center and weakens moving away from it.

Finding the direction: the right-hand rule. Point your thumb in the direction of the current; your fingers curl around the wire in the direction of the magnetic field lines.

Magnetic Force on a Moving Charge

Magnetic fields exert forces only on moving charges — unlike electric fields, which act on both stationary and moving charges.

When a charge moves through a magnetic field, it experiences a force:

FB = qvB sin θ

where FB is the magnetic force, q is the particle's charge, v is the magnitude of its velocity, B is the magnitude of the magnetic field, and θ is the smallest angle between the velocity vector and the field vector.

The force is directly related to the charge and speed of the particle, and to the field's strength — but the sin θ term means orientation matters too:

• At θ = 90° (velocity perpendicular to the field), the force is maximum, since sin 90° = 1.

• At θ = 0° (velocity parallel to the field), the force is zero, since sin 0° = 0.

Finding the direction. Point your fingers in the direction of the velocity of a positive charge, then curl them toward the direction of the magnetic field B — your thumb points in the direction of the magnetic force FB. For a negative charge, the force points in the opposite direction from what the rule indicates.

Magnetic Force on a Current-Carrying Wire

Since a current is simply a flow of moving charges, a current-carrying wire placed in a magnetic field also experiences a force:

FB = ILB sin θ

where FB is the magnetic force, I is the current in the wire, L is the length of wire within the field, B is the magnitude of the magnetic field, and θ is the angle between the current's direction and the field. As with a moving charge, the force is maximum at θ = 90° and zero at θ = 0°.

Finding the direction. This case uses a different hand orientation: point your thumb in the direction of the current I, curl your fingers toward the direction of the magnetic field B — your palm now points in the direction of the force FB. Reversing the current's direction (or dealing with negative charge flow) reverses the resulting force direction.

MCAT Callout — Right-Hand Rule, Two Versions: For a moving charge: fingers point along velocity, curl toward B, thumb gives force direction. For a current-carrying wire: thumb points along current, fingers curl toward B, palm gives force direction. Don't mix the two up — they use different starting fingers.

Common MCAT Mistakes

• Assuming magnetic fields act on stationary charges. They don't — magnetic forces act only on moving charges (or currents). A stationary charge sitting in a magnetic field feels zero magnetic force, no matter how strong the field.

• Mixing up the two right-hand rules. For a moving charge, fingers point along velocity and curl toward B, with the thumb giving the force direction. For a current-carrying wire, the thumb points along the current and fingers curl toward B, with the palm giving the force direction — these are different hand orientations, not interchangeable.

• Forgetting the sin θ dependence. Both FB = qvB sin θ and FB = ILB sin θ are zero when the charge's velocity (or the current) is parallel to the field (θ = 0°), even if B, q, v, I, and L are all large. Maximum force only occurs at θ = 90°.

• Confusing paramagnetic and ferromagnetic behavior. Both are attracted to an external field, but only ferromagnetic materials retain magnetism after the field is removed — paramagnetic materials' moments randomize again once the field is gone.

MCAT-Style Concept Check

Question: A proton (q = 1.6×10⁻¹⁹ C) moves at v = 2×10⁶ m/s perpendicular to a magnetic field of magnitude B = 0.5 T. What is the magnitude of the magnetic force on the proton?

• A) 8×10⁻¹⁴ N

• B) 1.6×10⁻¹³ N

• C) 1.6×10⁻¹⁹ N

• D) 3.2×10⁻¹³ N

Answer: B

Explanation: FB = qvB sin θ. Since the velocity is perpendicular to the field, θ = 90° and sin θ = 1. FB = (1.6×10⁻¹⁹)(2×10⁶)(0.5)(1) = 1.6×10⁻¹³ N.

FAQ

Do magnetic fields exert forces on stationary charges?

No. Magnetic forces act only on moving charges (or on currents, which are flows of moving charges). A charge at rest in a magnetic field experiences zero magnetic force.

What's the difference between diamagnetic, paramagnetic, and ferromagnetic materials?

Diamagnetic materials have all paired electrons and are weakly repelled by an external field. Paramagnetic materials have unpaired, randomly-oriented electrons and are weakly attracted. Ferromagnetic materials have unpaired electrons that self-align even without a field, are strongly attracted, and retain magnetism after the field is removed.

How do the two right-hand rules differ?

For a moving charge, point your fingers along the velocity and curl them toward B — your thumb gives the force direction. For a current-carrying wire, point your thumb along the current and curl your fingers toward B — your palm gives the force direction.

When is the magnetic force on a moving charge or current-carrying wire at its maximum?

At θ = 90°, when the velocity (or current) is perpendicular to the magnetic field, since sin 90° = 1. The force is zero when the velocity (or current) is parallel to the field (θ = 0°), since sin 0° = 0.