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

Answer:

e = 10 V

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

$e = - N\dfrac{d\phi}{dt}$

∅ = B . A

$e = - N\dfrac{d(BA)}{dt}$

$e = - NA\dfrac{dB}{dt}$

$e = - 10 \times 0.5 \times \dfrac{d}{dt}(3 + 2 t)$

$e = - 10 \times 0.5 \times 2$

e = -10 V

magnitude of induced emf

|e| = |-10 V|

e = 10 V

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