A rod of length 80 cm rotates about its mid point with a frequency of 10 rev/s. The potential difference in volts) between two ends of the rod due to a magnetic field, B=0.5 T directed perpendicular to the rod is

Options

A. `pi`
B. `1.6 pi`
C. `2 pi`
D. `0.8 pi`

Answer

D

Explanation

Given, frequency of revolution of the rod, f = 10 rev/s,
length of rod. 80 cm 0.8 m and magnetic field B = 0.5 T
Since, rod is rotated about its mid point, hence radius of circular revolution,
`r = L/2 = (0.8)/(2) = 0.4 m`
` therefore ` Potential difference between centre of rod and one end of rod due to revolution in magnetic is given by
V' = induced emf = `("change in flux")/("time taken")`
` (B.pi r^2)/(T) = B.pi r^2 . f " " [ because f = 1/T]`
` = 0.5 xx pi xx (0.4)^2 xx 10`
` = 0.8 pi`
` therefore ` Potential difference between two ends of rod due to revolution in the magnetic field,
`V = 2V' = 2 xx 0.8 pi = 1.6 pi`