Question

The flux of magnetic field through a closed conducting loop changes with time according to the equation, Φ = at2 + bt + c. (a) Write the SI units of a, b and c. (b) If the magnitudes of a, b and c are 0.20, 0.40 and 0.60 respectively, find the induced emf at t = 2 s.

Answer 1

Induced EMF is 1.2 V

Explanation:

According to the principle of homogeneity of dimensions, the dimensions of each term on both sides of a correct equation must be the same.

Now,  

$\Phi = at^2 + bt + c$

(a) The dimensions of the quantities $at^2$, bt, c and $\phi$ must be the same.

Thus, the units of the quantities are as follows:

a = $(\frac {\phi}{t^2}) = \frac {\phi/t}{t} = \frac {Volt}{s}$

b = $\frac {\phi}{t}$= Volt

c = [$\phi$] = weber

(b) The emf is written as:

E =  $\frac {d\phi}{dt} = 2at + b = 2\times 0.2\times 2 + 4$ (Bacause a = 0.2, b = 0.4 and c = 0.6)

On substituting t = 2 s, we get

E = 0.8 + 0.4  

  = 1.2 V which is value for induced emf.