Electromagnetic Effects

Straight wire. Current produces concentric circular field lines around the wire.

• Direction by right-hand grip rule: thumb points in current direction; fingers curl in field direction.

Coil / solenoid. A coil of wire carrying current has:

• Strong, roughly uniform field INSIDE the coil.
• Field lines outside resemble those of a bar magnet — with N and S poles at the ends.
• Direction: use the right-hand grip on the WIRE LOOP. Or: looking at one end, if current flows ANTICLOCKWISE → that end is N.

Strengthening a solenoid's field.

• More turns per metre.
• Higher current.
• A SOFT IRON CORE inside (greatly amplifies the field).

Electromagnet. A solenoid with a soft iron core. Switch the current on → magnet on. Switch off → magnet off (instant). Used in scrap-yard cranes, relays, electric bells.

Motor effect. When a current-carrying wire is placed in an EXTERNAL magnetic field, the wire experiences a force PERPENDICULAR to BOTH current and field.

Fleming's left-hand rule (predicts the force direction).

• Thumb: Force ($F$).
• First finger: B-field.
• Second finger: I (current). Hold them mutually perpendicular on your LEFT hand.

Reverse the current OR the field: force reverses too.

Force size depends on:

• Current size.
• Magnetic field strength.
• Length of wire in the field.
• Angle (max when wire is at 90° to the field).

DC motor. A coil in a magnetic field, with a split-ring commutator. Current in the coil creates forces on opposite sides → torque → rotation. Commutator reverses current direction every half-turn so the torque keeps pushing the same way → continuous rotation.

Worked qualitative. Why does a stronger magnet make the motor spin faster? Larger force on each side of the coil → larger torque → faster acceleration → higher final speed (limited by friction and back-EMF).

Faraday's law (qualitative). When the magnetic flux through a circuit changes, an EMF is induced.

Lenz's law. The induced current opposes the change that caused it.

Ways to induce current.

• Move a magnet into / out of a coil.
• Move the coil instead.
• Change the current in a NEARBY coil (mutual induction; basis of transformers).

Size of induced EMF depends on:

• Speed of the change (faster = larger EMF).
• Number of turns on the coil.
• Strength of the magnet.
• Area of the coil.

Direction (Lenz's law illustrated). Push the N pole of a magnet INTO a coil. The induced current creates a magnetic field that REPELS the incoming N pole — i.e. the coil end facing the magnet acts as N. Pull the magnet OUT and the coil end becomes S, attracting the magnet back.

Worked qualitative. Why does dropping a strong magnet down a copper tube fall slowly? As the magnet falls, the changing flux in the tube induces eddy currents that oppose the motion (Lenz). The drag slows the magnet — it "floats" through the tube.

AC generator. A rotating coil in a magnetic field. As the coil turns, the flux through it changes sinusoidally → induced EMF is sinusoidal → AC output. Slip rings (NOT split rings) connect the rotating coil to the external circuit.

Output: peak EMF when the coil sides are moving fastest across the field (parallel to it); zero when coil is parallel to the field.

Transformer. Two coils (primary $N_{p}$, secondary $N_{s}$) sharing a soft iron core. AC in the primary creates a changing flux in the core → induces an AC EMF in the secondary.

Equation. $\dfrac{V_{p}}{V_{s}} = \dfrac{N_{p}}{N_{s}}.$

Step-up: $N_{s} > N_{p}$, $V_{s} > V_{p}$. Used to raise voltage for transmission. Step-down: $N_{s} < N_{p}$, $V_{s} < V_{p}$. Used near homes to bring it back to safe levels.

Ideal transformer (100% efficient): $V_{p}I_{p} = V_{s}I_{s}$. Stepping voltage UP steps current DOWN by the same factor.

Worked. Step-up transformer: $N_{p} = 200$, $N_{s} = 1000$, $V_{p} = 230\,\text{V}$.

• $V_{s} = 230 \times 1000/200 = 1150\,\text{V}$.

Why high voltage for transmission? Power lost in cables = $I^{2}R$. Step UP voltage → step DOWN current → losses cut by current squared. National grid uses up to $400\,\text{kV}$.