Question

A flat coil of wire is used with an LC-tuned circuit as a receiving antenna. The coil has a radius of 0.30 m and consists of 420 turns. The transmitted radio wave has a frequency of 1.3 MHz. The magnetic field of the wave is parallel to the normal of the coil and has a maximum value of 1.7 x 10-13 T. Using Faraday's Law of electromagnetic induction and the fact that the magnetic field changes from zero to its maximum value in one-quarter of a wave period, find the magnitude of the average emf induced in the antenna in this time.

Answer 1

The average emf induce is
`V = 2.625 * 10^(-5) \ V`

Step-by-step explanation:

From the question we are told that

The radius of the coil is
`r = 0.30 \ m`

The number of turns is
`N = 420 \ turns`

The frequency of the transition radio wave is
`f = 1.3\ MHz = 1.3 *10^(6) Hz`

The magnetic field is
`B_,{max} = 1.7 * 10^(-13) \ T`

The time taken for the magnetic field to go from zero to maximum is
`\Delta T = (T)/(4)`

The period of the transmitted radio wave is
`T = (1)/(f)`

So

`\Delta T = (T)/(4) = (1)/(4 f)`

The potential difference can be mathematically represented as

`V = NA ((\Delta B)/(\Delta T) )`

`V = NA ([B_(max) - B_(min) ] * 4f)`

Where
`B_(min) = 0T`

substituting values

`V = 420 * (\pi *(0.30)^2) * (1.7 *10^(-13) * 4 * 1.3 *10^(6))`

`V = 2.625 * 10^(-5) \ V`