Manitude of the electric and magnetic field in an electromagnetic wave radiated by a `200 W` bulb at a distance 2m from it is assuming efficiency of bulb is `5%` and it behaves like a point source.

Options

A. `12.27 N//C, 4.09 xx 10^(-8) T`
B. `10 N//C, 10^(-5) T`
C. `11.7 N//C, 5 xx 10^(-6)T`
D. `5N//C, 10^(-4)T`

Answer

A

Explanation

Effective power of the bulb, `P = (5)/(100) xx 200 = 10W`
Intensity at distance r is given by
`I = (P)/(4pir^(2)) = (10)/(4 xx 3.14 xx 2^(3)) W//m^(2) = (10)/(16 xx 3.14) W//m^(2)`
`= 0.199 W//m^(2) = 0.2 W//m^(2)`
`I = (1)/(2)epsi_(0)E_(0)^(2)c`
`E_(0)^(2) = (2I)/(c xx E_(0))`
`rArr E_(0) = sqrt((2I)/(c xxepsi_(0)))`
`rArr E_(0) = sqrt((2xx 0.2)/(3 xx 10^(8) xx 8.85 xx 10^(-12))) rArr E_(0) = 12.27 N//C`
`rArr B_(0) = (E_(0))/(c) = (12.27)/(3 xx 10^(8)) = (12.27)/(3) xx 10^(-8) T = 4.09 xx 10^(-8) T`