Question

Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the magnitude of the emf (in V) that is induced in the loop if b = 14.0 A/s, h = 1.00 cm, w = 15.0 cm, and L = 1.05 m.

Answer 1

Answer:

$emf=81.51\times 10^{-7} Volt$

Explanation:

Given that

I = a + b t

b = 14 A/s , h= 1 cm , w= 15 cm , L= 1.05 m

The magnitude of induced emf is given as follows

$emf=\dfrac{d\phi}{dt}$

$emf=\dfrac{\mu_o\times L}{2\times \pi}\times ln\dfrac{h+w}{h}\times \dfrac{dI}{dt}$

I = a + b t

$\dfrac{dI}{dt}= b$

Now by putting the values in the above equation we get

$emf=\dfrac{4\times \pi \times 10^{-7}\times 1.05}{2\times \pi}\times ln\dfrac{1+15}{1}\times 14$

$emf=81.51\times 10^{-7} Volt$

Thus the induce emf will be

$emf=81.51\times 10^{-7} Volt$