# Electromagnetic Induction

## Electromagnetic Induction Revision

**Electromagnetic Induction**

When a** conductor** moves through a **magnetic field**, an **electromotive force (EMF)** is induced in the conductor. This is known as **electromagnetic induction**.

**Electromagnetic Induction**

As the conductor cuts through the **magnetic field lines**, it causes a **change in magnetic flux** which causes work to be done. This **energy **is transformed to **electrical energy**, causing a current to be **induced**. Importantly, this process can be harnessed in **transformers **and **generators**.

This phenomenon can be shown experimentally:

When the wire is **stationary** (either inside the magnetic field or outside), no voltage is shown on the sensitive voltmeter. This shows **no EMF is induced** as there is no change in **magnetic flux**.

When the wire is moved between the magnets, through the **magnetic field**, a reading can be seen on the voltmeter. This is because the wire **cuts the magnetic field lines** and causes a **change in magnetic flux**. Therefore an EMF is induced.

Moving the wire **faster**, **increasing the length **of the wire or **increasing the strength **of the magnets results in an increase in induced EMF as they all cause a **greater change in magnetic flux**.

**Faraday’s Law**

**Faraday’s law** can be observed in the experiment above. **Faraday’s law** states that magnitude of the induced EMF is proportional to the **rate of change of magnetic flux linkage**.

As previously shown, the **faster the wire moved **through the magnetic field, the** greater the strength of the magnet** or **the longer the wire**, all increase the magnitude of EMF produced as the all **increase the rate of change of magnetic flux linkage**.

**Lenz’s Law**

**Lenz’s Law** can also be shown experimentally. **Lenz’s law** states that the** induced EMF** acts in a direction to** oppose** the change that causes it.

**Lenz’s law** can be shown by passing a bar magnet through a coil of wire attached to a sensitive ammeter. The sensitive ammeter will **deflect in opposing directions** as the bar magnet is passed through the coil in opposite directions.

**Induced EMF**

By combining **Faraday’s law** and **Lenz’s law**, an equation can be formed to calculate the **induced EMF**:

\epsilon = -N \dfrac{\Delta \Phi}{\Delta t}

- \epsilon is the
**induced EMF**in volts \left(\text{V}\right). - N is the
**number of turns**on the coil. - \Delta \Phi is the
**change in magnetic flux**in Webers \left(\text{Wb}\right). - \Delta t is the
**change in time**in seconds \left(\text{s}\right).

The minus sign represents** Lenz’s law** as it shows the** direction** of the induced EMF will **oppose** the direction of the bar magnet.

**Example:** Calculate the EMF induced when a coil of wire with 200 turns creates a change in magnetic flux of 8 \times 10^{-6} \: \text{Wb} in 2 \: \text{ms}.

**[2 marks]**

\epsilon = -N \dfrac{\Delta \Phi}{\Delta t}

\epsilon = -200 \times \dfrac{8 \times 10^{-6}}{2 \times 10^{-3}}

\epsilon = -0.8 \: \text{V}

**Rotating Coil**

If a coil is rotating uniformly in a magnetic field, an EMF is induced. This is because we have a conductor that is constantly cutting the magnetic field lines, and the angle between the conductor and the field lines is constantly changing.

Using the principles of **circular motion**, the EMF induced as a result of this rotation can be calculated using the equation:

\epsilon = BAN \omega \sin \omega t

- \epsilon is the
**induced EMF**in volts \left(\text{V}\right). - B is the
**magnetic flux density**in Tesla \left(\text{T}\right). - A is the
**cross-sectional area**in metres squared \left(\text{m}^2\right). - N is the
**number of turns**on the coil. - \omega is the
**angular velocity**of the rotating coil \left(\text{rad s}^{-1}\right). - t is the
**tim****e**in seconds \left(\text{s}\right).

## Electromagnetic Induction Example Questions

**Question 1:** Describe a simple experiment that would allow you to demonstrate electromagnetic induction.

**[2 marks]**

Passing a **current carrying wire attached to a sensitive voltmeter through a magnetic field** will show electromagnetic induction. When the wire is stationary, no voltage is detected. As **the wire moves, a voltage is detected showing that an EMF is induced**.

**Question 2:** State Faraday’s law and Lenz’s law.

**[2 marks]**

**Faraday’s law**– the magnitude of the induced EMF is proportional to the rate of change of magnetic flux linkage.**Lenz’s law**– the direction of the induced EMF is such that it opposes the change that causes it.

**Question 3:** Calculate the EMF induced when a coil of wire with 400 turns creates a change in magnetic flux of 9 \times 10^{-6} \: \text{Wb} in 6 \: \text{ms}.

**[2 marks]**

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