﻿ In Thomson’s experiment for determining , the potential difference between the cathode and the anode (in the accelerating column) is the same as that between the deflecting plates (in the region of crossed fields). If the potential difference is doubled, by what factor should the magnetic field be increased to ensure that the electron beam remains undeflected? : Kaysons Education

# In Thomson’s Experiment For determining , The Potential Difference Between The Cathode And The Anode (in The Accelerating Column) Is The Same As That Between The Deflecting Plates (in The Region Of Crossed Fields). If The Potential Difference Is Doubled, By What Factor Should The Magnetic Field Be Increased To Ensure That The Electron Beam Remains Undeflected?

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## Question

### Solution

Correct option is

The charge to mass ratio of an electron is given by

Where V is the accelerating voltage between cathode and anode. Let d be the separation between the defecting plates. Now potential difference between the plates equals accelerating voltage V. Hence the electric field between the plates is

Using (ii) in (i) we get

If V is charged to V’ = 2VB must be increased to B’ given by

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