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`

Step-by-step 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 (d^2)/(4)`

=>
`A = 3.142 * (0.19^2)/(4)`

=>
`A = 0.0284 \ m^2`

At
`\delta t = 0.60 \ s`

The induced emf is

`\epsilon = - N * ([B_f - B_i ] * A )/(\delta t )`

=>
`\epsilon = - 40 * ([- 0.40 ] * 0.0284 )/(0.06)`

=>
`\epsilon = 7.57 \ V`

At
`\delta t = 6 \ s`

The induced emf is

`\epsilon = - N * ([B_f - B_i ] * A )/(\delta t )`

=>
`\epsilon = - 40 * ([- 0.40 ] * 0.0284 )/(6)`

=>
`\epsilon =0.0757 \ V`

At
`\delta t = 65 \ s`

The induced emf is

`\epsilon = - N * ([B_f - B_i ] * A )/(\delta t )`

=>
`\epsilon = - 40 * ([- 0.40 ] * 0.0284 )/(65)`

=>
`\epsilon =0.00699 \ V`