## Induced Voltage Formula :

Induced voltage is the induced voltage in ε _{(f/m)} in farads pe meter is equal to the is the total Number of turns of the loop and multiply the dΦ and product of the magnetic field _{B(N/A/T)} in Newton per meter per ampere or Tesla and divided by the _{dt(s)} in second. Hence the induced voltage can be written as

**ε _{(f/m)}=-N *dΦ_{B(N/A/T)/dt(s)}**

Where,

ε → induced voltage in farads per meter

N → total Number of turns of the loop

ΦB** = B.A **(Magnetic flux)

B → magnetic field in Newtons per meter per ampere or Tesla.

A → are the loop

T→ time in second

### Sum1 :

Calculate the induced voltage ? Consider a rectangular coil of 6 turns with a side length of 0.8m. This coil reaches the magnetic field0.5T within 20s.

### Solution :

Known value are

N=6

I=0.8m

B=0.5T

dt=20s

The formula for induced voltage is articulated as,

ε=-N dΦ_{B/dt}

Φ_{B}=B.A=0.5*0.8^{2}

=0.5*0.64=0.32T m^{2}

So, ε =-6*0.32/20=0.096V

Ε=0.096v

### Sum2 :

Consider a rectangular coil of 10 turns with a side length of 0.9m. This coil reaches the magnetic field0.4T within 40s.Compute the induced voltage?

### Solution :

Known value are

N=10

I=0.9m

B=0.4T

dt=40s

The formula for induced voltage is articulated as,

ε=-N dΦ_{B/dt}

Φ_{B}=B.A=0.4*0.9^{2}

=0.4*0.324=0.1296 m^{2}

So, ε =10*0.1296/40=0.0324V

Ε=0.0324 V