Two charges - q and + q are located at points 0 , 0 , - a and 0 , 0 , a respectively. How much work is done in moving a small test charge from the point 5 , 0 , 0 to - 7 , 0 , 0 along the x -axis? Does the answer change if the path of the test charge between the same points is not along the x -axis?

The given charges are forming a dipole, which is along z-axis. At a point on the x-y plane, the potential is zero as the point is equidistant from the positive and negative charges of equal magnitudes. Hence, the x-y plane forms an equipotential surface. The work done in this case is the change in potential energy of the system. As long as the initial and final points are on the x-y plane, the change in potential energy is zero, so the work done will also be zero irrespective of the path taken.

Figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for r a > > 1 , and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).

The figure showing the four charges is shown below. The distance between point P and Y is r . The system can be considered as a system with three charges, Charge + q placed at point X . Charge — 2 q placed at point Y . Charge + q placed at point Z . The distances X Y = Y Z = a , Y P = r , X P = r + a , Z P = r − a . Electrostatic potential caused by the system of three charges is, V = 1 4 π ∈ 0 q X P - 2 q Y P + q Z P = 1 4 π ∈ 0 q r + a - 2 q r + q r - a = q 4 π ∈ 0 r 2 - r a - 2 r 2 + 2 a 2 + r 2 + r a r r 2 - a 2 = q 4 π ∈ 0 2 a 2 r r 2 - a 2 = 2 q a 2 4 π ∈ 0 r 3 1 - a 2 r 2 As, r a ≫ 1 , ∴ a r < < 1 , a 2 r 2 is taken as negligible. ∴ V = 2 q a 2 4 π ∈ 0 r 3 Thus, it can be concluded that potential, V ∝ 1 r 3 . And we know that, for a dipole, V ∝ 1 r 2 . And we know that, for a monopole, V ∝ 1 r .

HARD

12th Assam Board

IMPORTANT

Earn 100

Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.

Important Questions on Electrostatic Potential and Capacitance

MEDIUM

12th Assam Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 2 - Electrostatic Potential and Capacitance>ADDITIONAL EXERCISES>Q 2.17

A long charged cylinder of linear charged density

λ

is surrounded by a hollow coaxial conducting cylinder. What is the electric field in the space between the two cylinders?

MEDIUM

12th Assam Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 2 - Electrostatic Potential and Capacitance>ADDITIONAL EXERCISES>Q 2.18

In a hydrogen atom, the electron and proton are bound at a distance of about $0.53 A^{°}$ . Estimate the potential energy of the system in $eV$ , taking the zero of the potential energy at infinite separation of the electron from proton. What is the value if the zero potential energy is taken at $1.06 A^{°}$ separation?

MEDIUM

12th Assam Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 2 - Electrostatic Potential and Capacitance>ADDITIONAL EXERCISES>Q 2.18

In a hydrogen atom, the electron and proton are bound at a distance of about

0.53 A^{°}

. What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the value of potential energy i.e.

- 27.2 eV

? What will be the answer if the zero potential energy is taken at

1.06 \overset{°}{A}

separation?

MEDIUM

12th Assam Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 2 - Electrostatic Potential and Capacitance>ADDITIONAL EXERCISES>Q 2.19

If one of the two electrons of a

H_{2}

molecule is removed, we get a hydrogen molecular ion

H_{2}^{+}

. In the ground state of an

H_{2}^{+}

, the two protons are separated by roughly

1.5 A^{°}

, and the electron is roughly

1 A^{°}

from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy

HARD

12th Assam Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 2 - Electrostatic Potential and Capacitance>ADDITIONAL EXERCISES>Q 2.2

Two charged conducting spheres of radii

a

and

b

are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.

MEDIUM

12th Assam Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 2 - Electrostatic Potential and Capacitance>ADDITIONAL EXERCISES>Q 2.21

Two charges

- q

and

+ q

are located at points

(0, 0, - a)

and

(0, 0, a)

respectively. What is the electrostatic potential at the points

(0, 0, Z)

and

(X, Y, 0)

? Obtain the dependence of potential on the distance

r

of a point from the origin when

r / a > > > 1

MEDIUM

12th Assam Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 2 - Electrostatic Potential and Capacitance>ADDITIONAL EXERCISES>Q 2.21

Two charges

- q

and

+ q

are located at points

(0, 0, - a)

and

(0, 0, a)

respectively. How much work is done in moving a small test charge from the point

(5, 0, 0)

(- 7, 0, 0)

along the x-axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?

HARD

12th Assam Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 2 - Electrostatic Potential and Capacitance>ADDITIONAL EXERCISES>Q 2.22

Figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on $r$ for $\frac{r}{a} > > 1$ , and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).

Question Image

Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.

Important Questions on Electrostatic Potential and Capacitance

Learn and Prepare for any exam you want !