Question

An electron moves along a metal tube with variable cross-section. The velocity of the electron when it approaches the neck of tube, is

a) Greater than ${{V}_{0}}$
b) Less Than ${{V}_{0}}$
c) Equal To ${{V}_{0}}$
d) Not defined

Answer 1

Hint: When an Electron moves in a Metal tube, It starts inducing positive charge on the surface of the metal tube. This Phenomenon is called Electrostatic Induction. When a moving charge is placed on a conducting material, an opposite charge is induced on the conducting material and this is called Electrostatic Induction.

Complete answer:
When an electron moves in the conducting tube, It starts inducing opposite charges on the surfaces of the conducting tube because of electrostatic induction.

Since there will be Positive charges on the surface of of the conducting metal tube , so they will try to attract the electron towards them and hence by the figure we know that the tube is narrower at the neck, hence we can say that the force of attraction will be more toward the neck of the tube and therefore the electron will start accelerating toward the neck.

Due to this acceleration the speed of the electron will get increased and hence its speed will be greater than its original speed.

So we can say that option A is correct which shows that the speed will be greater than ${{V}_{0}}$.

Note:
If there was a proton accelerating instead of electron then also the same thing will happen and Electrostatic induction will take place which will induce the opposite charges on the surface of tube ( negative charges in case of proton) and hence for that also option A will be correct because those negative charges will attract proton and the proton will start accelerating.