# Induced Voltage Formula

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. Induced voltage is described by making use of the Faraday’s law of induction. Induced voltage of a closed-circuit is described as the rate of change of magnetic flux through that closed circuit. 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, Magnetic flux, ΦBΦB = B.A, (B is the magnetic field and A is the area of the loop), t is the time.

Induced Voltage Solved Examples

Solved questions of induced voltage is provided below:

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

Known values are,
N = 5, l = 0.5m, B = 0.3T, dt = 10s
The formula for induced voltage is articulated as,

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

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

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

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

Problem  2: Imagine a circular loop of radius 0.05m and the magnetic field of 0.5T is attained by 8s. Compute the induced voltage if there are 10 number of turns?

Given parameters are,
N = 10, r = 0.05m, B = 0.5T, dt = 8s
The formula for induced voltage is articulated by,

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

$\dpi{120}&space;\large&space;\Phi&space;_{B}=B.A=3.0\times0.52^{2}$

$\dpi{120}&space;\large&space;0.5\times3.14\times0.05^{2}$

$\dpi{120}&space;\large&space;=0.003925Tm^{2}$

$\dpi{120}&space;\large&space;\varepsilon&space;=-10\times\frac{0.003925}{8}=0.00490V$