Answers to Problems on Electric Field and Potential HC Verma's Questions for Short Answer

Q#1

The charge on a proton is +1.6 x 10⁻¹⁹ C and that on an electron is -1.6 x 10⁻¹⁹ C. Does it mean that the electron has a charge 3.2 x 10⁻¹⁹ C less than the charge of a proton? 

Answer: 

No. Here it means that the charge on a proton is equal to that on an electron but the nature of the charge is opposite.   

Q#2

Is there any lower limit to the electric force between two particles placed at a separation of 1 cm?  

Answer: 

The electric force between two particles is given as Kq₁q₂/r². K is a constant and r = 1 cm also constant in this case, hence the lowest limit of the electric force will be when q₁ and q₂ are lowest. Since the lowest possible charge on a particle will be equal to that on one electron or one proton i.e. = e. Hence the lower limit of electric force between two particles = Ke²/r². Attraction or repulsion. 

Q#3

Consider two particles A and B having equal charges and placed at some distance. The particle A is slightly displaced towards B. Does the force on B increase as soon as the particle A is displaced? Does the force on the particle A increase as soon as it is displaced?  

Answer: 

The interaction between electrically charged particles is due to the electric field around them. These fields can travel with a velocity of light. Since particle A can not be displaced more quickly than the speed of light hence the answers for both the questions are yes. 

Q#4

Can a gravitational field be added vectorially to an electric field to get a total field?  

Answer: 

No. Both types of fields are totally different in nature and do not interact with each other.   

Q#5

Why does a phonograph-record attract dust particles just after it is cleaned? 

Answer: 

When the record is cleaned it gets electrically charged due to rubbing. Hence it attracts dust particles by induction or those particles which have an opposite charge from the record.    

Q#6

Does the force on a charge due to another charge depend on the charges present nearby?  

Answer: 

No. The force on a charge due to another charge is fully independent of the charges present nearby.   

Q#7

In some old text, it is mentioned that 4π lines of force originate from each unit positive charge. Comment on the statement in view of the fact that 4π is not an integer. 

Answer: 

The total solid angle around a point is 4π steradians. Though 4π is not an integer it signifies the all-round space about a unit positive charge where these lines of forces are equispaced. 

Q#8

Can two equipotential surfaces cut each other?   

Answer: 

An equipotential surface is the surface on which each point has the same potential. Two equipotential surfaces will be for two different potentials. They can not cut each other because if they do there will be two different potentials at the points where they cut which will be outright wrong.  

Q#9

If a charge is placed at rest in an electric field, will its path be along a line of force? Discuss the situation when the line of forces are straight and when they are curved. 

Answer: 

It will depend upon the natutre of the line of force, whether it is straight or curved. When the charge is placed at rest in the electric field, the force on the charge is along the tangent drawn on the line of force at that point. When the charge is released it starts to move along the direction of the force.

Now for the straight line of force, the movement of the charge and the force is always along the straight line.

Thus, its path will be along the line of force. See the point P in diagram below.

For the curved line of force, the charge starts to move along the force, the direction of which is tangential to the line of force (At point A). This force will accelerate it and the charge will very soon get some velocity.

At this point the charge will have a force along the tangent (Force F at point B) and due to the curvature this direction of the force is not the same direction when the charge was releaed.

Also now there is another force of inertia due to the motion (Force F') acting on it and its direction will be along the velocity attained.

So, the charge will move along the resultant (Force R) of the two forces and not along the line of the electric force.     

Q#10

Consider the situation shown in figure (29 - Q1). What are the signs of q₁ and q₂? If the lines are drawn in proportion to the charge, what is the ratio q₁/q₂?

Answer: Since the lines are entering q₁ it is a negative charge. The lines are emerging out of q₂ hence it is a positive charge. 

If the lines are drawn proportional to the charge, we see 6 lines entering q₁ and 18 lines emerging out of q₂.

Thus, the ratio

q₁/q₂ = 6/18 = 1/3

 Q#11

A point charge is taken from point A to point B in an electric field. Does the work done by the electric field depend on the path of the charge?  

Answer: 

No, the work done by the electric field depends only on the potential difference between the points A and B. It is independent of the path of the charge.   

Q#12

It is said that the separation between the two charges forming an electric dipole should be small. The small compared to what?  

Answer: 

The separation between the two charges forming an electric dipole should be small compared to the distance of the point from the center of the dipole where we intend to find the field due to the dipole.   

Q#13

The number of electrons in an insulator is of the same order as the number of electrons in a conductor. What is then the basic difference between a conductor and an insulator? 

Answer: 

The basic difference between a conductor and an insulator is that the electrons can move freely in a conductor but they can not move to long distance s in an insulator due to more rigid bonding in the molecules.  

Q#14

When a charged comb is brought near a small piece of paper, it attracts the piece. Does the paper become charged when the comb is brought near it?  

Answer: 

No, the paper does not get charged, only the electrons in the paper are rearranged. The concentration of opposite charge to the comb becomes more at the near end that is why it is attracted towards the comb. The net charge on the paper remains the same.