Question

A 11.0 nC charge is at x = 0cm and a -1.3 nC charge is at x = 5 cm .

At what point or points on the x-axis is the electric potential zero?

Answer 1

The diagram for the given situation is shown below :

Here,  

Distance between both the charges are 5 cm or 0.05 m .

Electric potential due to a charge particle having charge ' Q ' at a distance ' r ' is given by

  

Let at a distance x from the origin i.e. at the point C (x, 0), the net potential (due to both the charges) is zero.

Case I : If the point C is between the two charges

Electric potential due to the 11 nC charge at the point C (x, 0) is

  

Electric potential due to the charge ' q ' at the point C (x , 0) is

  

Therefore,

or,

or,   

or,   

or,   

or,   

or,

Case II : If the point C is in right of the charge q (charge at A)

Electric potential due to the 11 nC charge at the point C (x, 0) is

  

Electric potential due to the charge ' q ' at the point C (x , 0) is

  

Therefore,

or,

or,   

or,   

or,   

or,   

or,

Case III : If the point C is in left of the charge Q (i.e. charge at A)

Electric potential due to the 11 nC charge at the point C (x, 0) is

  

Electric potential due to the charge ' q ' at the point C (x , 0) is

  

Therefore,

or,

or,   

or,   

or,   

or,   

or,

The negative sign is indicating that , the position we have taken should be at 5.67 cm right from the charge Q .

This is same as the result of case II .

Hence the only possible cases are at the points (4.47 , 0) and (5.7 , 0) in cm . i.e. at (4.47 , 0 ) and (5.67 , 0) the net potential will be zero.

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