Question

In Thomsons experiment for determining e/m, the potential difference between the cathode and the anode is same as that between the deflecting plates ( in the region of crossed fields). If the potential difference is doubled. Then the factor by which the magnetic field be increased to ensure that the electron beam remains undeflected is:

• A. $\sqrt{2}$
• B. 2
• C. $2\sqrt{2}$
• D. 4

Answer 1

The correct option is A $\sqrt{2}$

Speed for Thomson experiment $=\sqrt{\frac{2eV}{m}}=Ve$
In the tube,
$E=\left(Ve\right)B$ -------------------------(I)
If the potential difference is double i.e. E is doubled,
New velocity $=\left(V{e}_1\right)=\sqrt{2}{V}_e$
So,
Increase of B for (I) to satisfy,
$B_{new}=\sqrt{2}B$