Magnetism and electromagnetism connect electric current, magnetic fields, forces, and energy transfer. This cheat sheet helps students organize the main equations used in force, field, flux, induction, motor, and transformer problems. It is useful for quickly checking which angle, direction rule, and unit belong with each formula.
Students in grades 10-12 need these relationships for circuits, motion in fields, generators, and electromagnetic induction.
Key Facts
- The magnetic force on a moving charge is , where is the angle between the velocity and magnetic field .
- The magnetic force on a current-carrying wire is , where is the length of wire inside the magnetic field.
- The magnetic field around a long straight wire is , where is the distance from the wire.
- The magnetic field inside a long solenoid is approximately , where is the number of turns per meter.
- Magnetic flux through a flat loop is , where is measured between and the area vector perpendicular to the loop.
- Faraday's law gives induced emf as , and the negative sign shows the direction described by Lenz's law.
- The torque on a rectangular current loop in a uniform magnetic field is .
- For an ideal transformer, and .
Vocabulary
- Magnetic field
- A magnetic field is a region where moving charges, currents, or magnetic materials experience magnetic forces, represented by the vector .
- Magnetic flux
- Magnetic flux measures how much magnetic field passes through an area, calculated with for a uniform field.
- Electromagnetic induction
- Electromagnetic induction is the production of an emf or current when the magnetic flux through a circuit changes.
- Lorentz force
- The Lorentz force is the total electromagnetic force on a charge, written as .
- Solenoid
- A solenoid is a coil of wire that creates a strong, nearly uniform magnetic field inside when current flows through it.
- Lenz's law
- Lenz's law states that an induced current flows in the direction that opposes the change in magnetic flux that caused it.
Common Mistakes to Avoid
- Using instead of for magnetic force is wrong because and depend on the component perpendicular to the magnetic field.
- Measuring the flux angle from the surface of the loop is wrong because uses the angle between and the area vector, which is perpendicular to the surface.
- Ignoring the negative sign in is wrong because it represents Lenz's law and determines the direction of the induced current.
- Applying inside a solenoid is wrong because that formula is for a long straight wire, while a long solenoid uses .
- Reversing transformer ratios is wrong because voltage follows turns with , while current follows the inverse ratio in an ideal transformer.
Practice Questions
- 1 A charge of moves at perpendicular to a magnetic field of . Find the magnetic force magnitude.
- 2 A wire of length carries current at to a magnetic field of . Calculate the force on the wire.
- 3 A coil has turns and its magnetic flux changes from to in . Find the magnitude of the induced emf.
- 4 A loop is pulled out of a region with a uniform magnetic field. Explain how Lenz's law predicts the direction of the induced current and why the induced field opposes the change.
Understanding Magnetism & Electromagnetism
Magnetic fields are regions where magnets or electric currents can affect certain objects and moving charges. Field lines are a drawing tool, not real threads in space. Their direction shows the direction a tiny north magnetic pole would point.
Closer lines represent a stronger field. Inside a bar magnet, many microscopic magnetic regions called domains are lined up.
In an unmagnetized piece of iron, domains point in many directions, so their effects mostly cancel. A compass responds to Earth’s magnetic field, which is why its needle settles in a north to south direction.
A magnetic field does not push every charge in the same way. A charge at rest feels no magnetic force from the field alone. The force appears when the charge moves across the field.
This force is sideways, perpendicular to both the motion and the field direction. That sideways force can bend the path of an electron or proton into a circle. The direction reverses for a negative charge.
This is a common source of mistakes. Right hand rules usually give the direction for conventional current or a positive charge. For electrons, the final direction must be reversed.
Electromagnetic induction depends on change. A loop can sit in a steady magnetic field without producing a lasting induced voltage. A voltage appears when the amount of field passing through the loop changes.
Moving a magnet, rotating a coil, changing the coil area, or changing the field strength can cause this change. The induced current creates its own magnetic effect that opposes the change that produced it. This is not an arbitrary direction rule.
It follows conservation of energy. If induction helped the change instead of resisting it, a system could gain energy without an input.
Motors and generators use the same interaction in opposite ways. A motor sends current through coils in a magnetic field, producing a turning effect. A generator turns coils mechanically, producing electrical energy.
Transformers transfer energy between coils through a changing field in an iron core. They need alternating current because a constant current creates no continuing change in magnetic flux. When solving problems, first sketch the field direction, the motion or current direction, and the angle being measured.
Check whether the angle is to the field itself or to a line perpendicular to a surface. Keep units consistent, especially tesla for field strength, weber for flux, and volt for induced voltage.