Question

In Thomson's experiment, the same H.T. supply provides potential to the anode, as also to the positive deflecting plate in the region of crossed fields. If the supply voltage is doubled, then the value of new magnetic field to keep the electron beam undeflected will be

• A. $2B$
• B. $B$
• C. $\sqrt{B}$
• D. $\frac{B}{2}$

Answer 1

The correct option is A $2B$

For the electron beam to be undeflected the resultant force should be parallel to cathode rays.
So, the magnetic force which is perpendicular to velocity must be nullified by transverse electric force. i.e., $F_e=F_b$ .
So, $\frac{qV}{d}=qvB$
which can be simplified as $V\alpha B$ when q,v and d are constant.
Given $\frac{V_f}{V_i}=2$ (where suffix i,f represent initial and final quantities respectively)
So by substituting and solving this, $\frac{V_f}{V_i}=\frac{B_f}{B_i}=2$ and $B_f=2B$