Question

A continuous length of wire is made into 10 coaxial loops, located in the plane of this page. Each loop has a cross sectional area of 0.5 m2. A uniform time-varying magnetic field is directed into the page and its magnitude is given by B = 3T + (2T/s)*t. What is the induced potential difference in the loop and the direction of the induced current at t = 2.0 s?

Answer 1

e = 10 V

Step-by-step explanation:

given,

number of the coaxial loops = 10

Cross sectional area = 0.5 m²

magnitude of magnetic field =

B = 3 T + (2 T/s)*t.

B = ( 3+ 2 t ) T

induced potential difference = ?

At time = 2 s

we know,

induced emf

`e = - N(d\phi)/(dt)`

∅ = B . A

`e = - N(d(BA))/(dt)`

`e = - NA(dB)/(dt)`

`e = - 10 * 0.5 * (d)/(dt)(3 + 2 t)`

`e = - 10 * 0.5 * 2`

e = -10 V

magnitude of induced emf

|e| = |-10 V|

e = 10 V

the induced potential difference in the loop = e = 10 V