Question

A 40-turn coil has a diameter of 19 cm. The coil is placed in a spatially uniform magnetic field of magnitude 0.40 T so that the face of the coil and the magnetic field are perpendicular. Find the magnitude of the emf induced in the coil (in V) if the magnetic field is reduced to zero uniformly in the following times.

Answer 1

Complete Question

The  complete question is shown on the first uploaded image  

Answer:

a

 $\epsilon = 7.57 \ V$

b

 $\epsilon =0.0757 \ V$

c

  $\epsilon =0.00699 \ V$

Explanation:

From the question we are told that  

  The number of turns is  N  =  40  turns  

   The  diameter is  $d = 19 \ cm = 0.19 \ m$

    The initial  magnetic field is $B_i = 0.40 \ T$

    The final magnetic field is $B_f = 0 \ T$  

Generally the cross-sectional area of the coil is mathematically represented as

       $A = \pi \frac{d^2}{4}$

=>    $A = 3.142 * \frac{0.19^2}{4}$

=>    $A = 0.0284 \ m^2$

At $\delta t = 0.60 \ s$

The  induced emf is  

        $\epsilon = - N * \frac{[B_f - B_i ] * A }{\delta t }$

=>    $\epsilon = - 40 * \frac{[- 0.40 ] * 0.0284 }{0.06}$

=>   $\epsilon = 7.57 \ V$

At $\delta t = 6 \ s$

The  induced emf is  

        $\epsilon = - N * \frac{[B_f - B_i ] * A }{\delta t }$

=>    $\epsilon = - 40 * \frac{[- 0.40 ] * 0.0284 }{6}$

=>   $\epsilon =0.0757 \ V$

At $\delta t = 65 \ s$

The  induced emf is  

        $\epsilon = - N * \frac{[B_f - B_i ] * A }{\delta t }$

=>    $\epsilon = - 40 * \frac{[- 0.40 ] * 0.0284 }{65}$

=>   $\epsilon =0.00699 \ V$