In a Thomson's set up for elm, the same high tension d.c. supply provides potential to anode for acceleration and also the positive voltage to the deflecting plate in the region of crossed fields. If the supply voltage is doubled, by what factor the magnetic field be increased to keep the electron beam undeflected ?

Options

A. 2 times
B. `sqrt2` times
C. `(1)/(sqrt(1))` times
D. `(1)/(2)` times

Answer

B

Explanation

Here `(e)/(m)=(E^(2))/(2VB^(2))=(V^(2))/(2Vd^(2)B^(2))=(V)/(2d^(2)B^(2))`
If potential is changed to 2V, let them magnetic field to B.
then `(e)/(m)=(2V)/(2d^(2)B.^(2)) or(2V)/(2d^(2)B.^(2))=(V)/(2d^(2)V^(2))`
or `B.^(2)=2B^(2) or B.= sqrt(2)B`