Question

A UHF antenna is oriented at an angle of 47o to a magnetic field that changes at a rate of 0.23 T/s. What is the induced emf of the antenna if it has a diameter of 13.4 cm? O 5.4 mV ? 2.2 ? 0027 ?

Answer 1

Induced emf,
`\epsilon=2.2\ mV`

Step-by-step explanation:

It is given that,

Rate of change of magnetic field,
`(dB)/(dt)=0.23\ T/s`

A UHF antenna is oriented at an angle of 47° to a magnetic field, θ = 47°

Diameter of the antenna, d = 13.4 cm

Radius, r = 6.7 m = 0.067 m

We need to find the induced emf of the antenna. It is given by :

`\epsilon=-(d\phi)/(dt)`

Where

`\phi` = magnetic flux,
`\phi=BA\ cos\theta`

So,
`\epsilon=(d(BA\ cos\theta))/(dt)`

B = magnetic field

`\epsilon=A(d(B))/(dt)\ cos\theta`

`\epsilon=\pi r^2* (dB)/(dt)* cos(47)`

`\epsilon=\pi (0.067\ m)^2* 0.23\ T-s* cos(47)`

`\epsilon=0.0022\ V`

`\epsilon=2.2\ mV`

So, the induced emf of the antenna is 2.2 mV. Hence, this is the required solution.