 # Induced Voltage Formula

The induced voltage is produced as a product of electromagnetic induction. Electromagnetic induction is the procedure of producing emf (induced voltage) by exposing a conductor into a magnetic field. The induced voltage is described by making use of Faraday’s law of induction. The induced voltage of a closed-circuit is described as the rate of change of magnetic flux through that closed circuit.

## Formula of Induced Voltage

The induced voltage formula is articulated as,

$$\begin{array}{l}\varepsilon = -N\frac{d\Phi_B}{dt}\end{array}$$

Where,

• ε is the induced voltage
• N is the total number of turns of the loop

ΦB = B.A (Magnetic flux)

• B is the magnetic field
• A is the area of the loop
• t is the time

### Induced Voltage Solved Example

The solved question of induced voltage is given below:

Problem 1: Consider a rectangular coil of 5 turns with a side length of 0.5 m. This coil reaches the magnetic field 0.3T within 10s. Compute the induced voltage?

Known values are,
N = 5

l = 0.5 m

B = 0.3T

dt = 10s

The formula for induced voltage is articulated as,

$$\begin{array}{l}\varepsilon = -N\frac{d\Phi_B}{dt}\end{array}$$
$$\begin{array}{l}\Phi_B = B\cdot A = 3\times 0.5^2\end{array}$$
$$\begin{array}{l}=0.3\times 0.25 = 0.075\ Tm^2\end{array}$$

So,

$$\begin{array}{l}\varepsilon = -5\times \frac{0.075}{10}=-0.0375\ V\end{array}$$