Question

A 800 turn coil of effective area 0.05 m² is kept perpendicular to a magnetic field 5 × 10⁻⁵ T. When the plane ofthe coil is rotated by 90º around any of its coplanar axis in 0.1 s, the emf induced in the coil will be :
(1) 2 V
(2) 0.2 V
(3) 2 × 10⁻³ V
(4) 0.02 V

Answer 1

The emf induced in the coil will be 0.02V.

Step by step explanation:

Change in magnetic flux makes an emf induced in the coil.

Change in magnetic flux can be calculated by the following formula.

                    $\bold{\Delta\phi =NBAcos90^{o}-BACos0^{o}}$

                          $\bold{\Rightarrow -NBA}$..................(1)

From the given,

Number of turns in coil = N = 800

Area of coil = A = $0.05m^{2}$

Magnetic field= B = $5\times 10^{-5}T$

Time taken to rotate = $\Delta T = 1$

Initial angle = $\Theta _{1}=0^{o}$

Final angle = $\Theta _{2}=90^{o}$

Substitute the all given values in equation (1)

                  $\Rightarrow 800\times 5\times 10^{-5}\times 0.05$

                 $\Rightarrow -2\times 10^{-3}weber$

Hence, $\Delta\phi =-2\times 10^{-3}weber$

Induced emf can be calculated by the following formula.

                 $\bold{e=\frac{- \Delta\phi}{\Delta t}}$

                  $\Rightarrow \frac{-(-2\times 10^{-3}Wb)}{0.1s}=0.02V$

Therefore, The emf induced in the coil will be 0.02V.

Hence, correct option is 4

Answer 2

Given :

The number of turns of coil = N = 800

The effective area of coil = A = 0.05 sq meters

The magnitude of magnetic field is placed perpendicular  = B = 5 × 10⁻⁵ T

The time for change in flux = Δt= 0.01 sec

To Find :

The EMF induced in coil

Solution :

The emf induced in coil, when flux change at given period of time

i.e  EMF =  - $\dfrac{\Delta \phi }{\Delta t}$

Now, Change in flux =  Δ∅ = $\phi _2 - \phi _1$

The field is perpendicular to area, and initially ate angle  0°

So,   Δ∅ = NAB cos 0° - NAB cos 90°

                = - NAB - ( 0 )

                = - NAB

i.e        Δ∅ = - NAB

Or  ,      Δ∅ = - 800 × 0.05 m² ×  5 × 10⁻⁵ T

                   =  - 40 ×  5 × 10⁻⁵ T

                   = -  2  × $10^{-3}$ T

                   =  - 0.002 Tesla

So, Change in flux = - 0.002 Tesla

Again ,

Emf induced in coil, when flux change at given period of time

∵    EMF = - $\dfrac{\Delta \phi }{\Delta t}$

Or, EMF = - ( $\dfrac{-0.002}{0.1}$ )

∴   EMF = 0.02 volt

Hence, The Emf induced in coil, when flux change at given period of time is 0.02 volts  Answer