Question

A radio wave is traveling toward the North, polarized with its electric field in the vertical plane and its magnetic field in the horizontal plane. It has wavelength 2.8 m and intensity 1. 4 W/m2 . You would like to detect this wave by induction using a circular loop antenna of radius 0.25 m. (a) How should the loop be oriented so as to produce maximum induced emf? (b) What is that maximum induced emf? You may assume that the loop is small enough so that the magnetic field at any instant is approximately uniform across the loop

Answer 1

Part a)

Loop must be in Perpendular of Magnetic Field (Horizontal plane) so that angle between Magnetic Field and Area of Loop (is considered in Normal/perpendicular direction) is Zero so that there could be maximum value of Magnetic Flux "B.A" and Emf (rate of change of Flux will be maximum as well)

Part b)

As we know that Intensity of EM wave will be

I = cB² / (2*μ_o) ; where c is speed of light, B is maximum magnetic Field,

B² = 2* I *μ_o /c

B = SQRT (2* I *μ_o /c)

= SQRT ( 2 * 1.4 * 4π * 10^-7 /(3 * 10⁸))

B = 1.08 * 10^-7 T

Maximum Induced EMF will be

B * A  

= 1.08 * 10^-7 * (π * 0.25²)

= 2.13 * 10^-8 V