Q: Consider the situation shown in the figure. What are the signs of q1 and q2 ? If the lines are drawn in proportion to the charges, what is the ratio q1/q2 ?

The electric lines of force are entering charge q1 ; so, it is negative. On the other hand, the lines of force are originating from charge q2 ; so, it is positive. If the lines are drawn in proportion to the charges, then q2q1=186 ⇒q2q1=31 6 lines are entering q1 and 18 are coming out of q2 .

Question 1

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

Accepted Answer

An electron and a proton have equal and opposite charges of magnitude 1.6×10−19 C. But it doesn't mean that the electron has 3.2×10−19 C​ less charge than the proton.

Question 2

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

Accepted Answer

Yes, there's a lower limit to the electric force between two particles placed at a separation of 1 cm, which is equal to the magnitude of force of repulsion between two electrons placed at a separation of 1 cm.

Question 3

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

Accepted Answer

Electrostatic force follows the inverse square law, F=K/r2. This means that the force on two particles carrying charges increases on decreasing the distance between them. Therefore, as particle A is slightly displaced towards B, the force on B as well as A will increase.

Question 4

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

Accepted Answer

No, a gravitational field cannot be added vectorially to an electric field.This is because for electric influence, one or both the bodies should have some net charge and for gravitational influence both the bodies should have some mass. Also, gravitational field is a weak force,while electric field is a strong force.

Question 5

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

Accepted Answer

When a phonograph record is cleaned, it develops a charge on its surface due to rubbing. This charge attracts the neutral dust particles due to induction.

Question 6

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

Accepted Answer

Coulomb's Law states that the force between two charged particle is given byF=4πϵ0​r2q1​q2​​ whereq1​  and q2​  are the charges on the charged particlesr=  separation between the charged particlesϵ0​=  permittivity of free spaceAccording to the Law of Superposition, the electrostatic forces between two charged particles are unaffected due to the presence of other charges.

Question 7

In some old texts 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.

Accepted Answer

4π is the total solid angle. "4π lines of force" is just a way of stating that the field lines extend uniformly in all directions away from the charge.

Question 8

Can two equipotential surfaces cut each other?

Accepted Answer

At the point of intersection, two normals can be drawn. Also, we know that electric field lines are perpendicular to the equipotential surface. This implies that at that point two different directions of the electric field are possible, which is not possible physically. Hence, two equipotential surfaces cannot cut each other.

Question 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 lines of force are straight and when they are curved.

Accepted Answer

If a charge is placed at rest in an electric field, its path will be tangential to the lines of force. When the electric field lines are straight lines then the tangent to them will coincide with the electric field lines so the charge will move along them only. When the lines of force are curved, the charge moves along the tangent to them.

Question 10

Consider the situation shown in the figure. What are the signs of q1​  and q2​ ? If the lines are drawn in proportion to the charges, what is the ratio q1​/q2​ ?

Accepted Answer

The electric lines of force are entering charge q1​ ; so, it is negative. On the other hand, the lines of force are originating from charge q2​ ; so, it is positive. If the lines are drawn in proportion to the charges, then q2​q1​​=186​  ⇒q2​q1​​=31​ 6 lines are entering q1​  and 18 are coming out of q2​ .

Question 11

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

Accepted Answer

Electrostatic field is a conservative field. Therefore, work done by the electric field does not depend on the path followed by the charge. It only depends on the position of the charge, from which and to which the charge has been moved.

Question 12

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

Accepted Answer

The separation between the two charges forming an electric dipole should be small compared to the distance of a point from the centre of the dipole at which the influence of the dipole field is observed.

Question 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 ?

Accepted Answer

The outer electrons of an atom or molecule in a conductor are only weakly bound to it and are free to move throughout the body of the material. On the other hand, in insulators, the electrons are tightly bound to their respective atoms and cannot leave their parent atoms and move through a long distance.

Question 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?

Accepted Answer

When a charged comb is brought near a small piece of paper, it attracts the piece due to induction. There's a distribution of charges on the paper. When a charged comb is brought near the pieces of paper then an opposite charge is induced on the near end of the pieces of paper so the charged comb attracts the opposite charge on the near end of paper and similar on the farther end. The net charge on the paper remains zero.

Question 15

Figure shows some of the electric field lines corresponding to an electric field. The figure suggests that

Accepted Answer

(c) EA​=EC​>EB​.The crowding of electric field lines at a point shows the strength of the field at that point. More the crowding of field lines, more will be the field strength. At points A and C, there's equal crowding, whereas at point B, the lines are far apart. Therefore, EA​=EC​>EB​.

Question 16

When the separation between two charges is increased, the electric potential energy of the charges:

Accepted Answer

(d) May increase or decrease.The electric potential energy, E, between the two charges, q1​  and q2​ , separated by the distance, r, is given as E=K(q1​q2​)/r ,Where k = constant As the distance between the charges is increased, the energy will decrease if both the charges are of similar nature. But if the charges are oppositely charged, the energy will become less negative and, hence, will increase.

Question 17

If a positive charge is shifted from a low-potential region to a high-potential region, the electric potential energy:

Accepted Answer

(a) Increases.The electric potential energy, E, of a positive charge, q, in a potential, V, is given by E = qV. As the charge is moved from a low-potential region to a high-potential region, i.e. as V is increased, E will increase.

Question 18

Two equal positive charges are kept at points A and B. The electric potential at the points between A and B (excluding these points) is situated while moving from A to B. The potential:

Accepted Answer

(d) Decreases then increases.Let the distance between the points A and B be r. Let us take a point P at a distance x from A (x Electric potential V at point P due to two charges of equal magnitude q is given byV=4π∈0​xq​+4π∈0​(r−x)q​⇒V=4π∈0​x(r−x)qr​ Now, differentiating V with respect to x, we get⇒V=4π∈0​x(r−x)qr​Therefore, x = r/2.It can be observed that  dxdV​=4π∈0​x2(r−x)2−qr(r−2x)​  for x x = r/2, the potential is minimum.As dxdV​<0  for x > r/2, the potential is increasing after x = r/2.

Question 19

The electric field at the origin is along the positive x-axis. A small circle is drawn with the centre at the origin, cutting the axes at points A, B, C and D with coordinates (a, 0), (0, a), (−a, 0), (0, −a), respectively. Out of the points on the periphery of the circle, the potential is minimum at:

Accepted Answer

AThe potential due to a charge decreases along the direction of electric field. As the electric field is along the positive x-axis, the potential will decrease in this direction. Therefore, the potential is minimum at point (a,0).

Question 20

If a body is charged by rubbing it, its weight:

Accepted Answer

(d) May increase slightly or may decrease slightly.If a body is rubbed with another body, it'll either gain some electrons from the other body and become negatively charged or it'll lose some electrons to the other body and become positively charged. Gain of electrons increases the weight of a body slightly and loss of electrons reduces the weight slightly.

Chapter 7 : Electric Field and Potential