# 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,

$\dpi{120}&space;\large&space;\varepsilon&space;=-N\frac{d\Phi_{B}&space;}{dt}$

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,

$\dpi{120}&space;\large&space;\varepsilon&space;=-N\frac{d\Phi_{B}&space;}{dt}$

$\dpi{120}&space;\large&space;\Phi&space;_{B}=B.A=0.3\times0.5^{2}$

$\dpi{120}&space;\large&space;=0.3\times0.25=0.075Tm^{2}$

$\dpi{120}&space;\large&space;So,\varepsilon&space;=-5\times\frac{0.075}{10}=-0.0375V$