Explain why two field lines never cross each other at any point?

What is the net flux of the uniform electric field of Exercise 1.14 through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?

The electrostatic force on a small sphere of charge $0.4 \mu C$ due to another small sphere of charge $-0.8 \mu C$ in air is 0.2 N. (b) What is the force on the second sphere due to the first?

Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is $6.5 \times 10^{-7}$ C? The radii of A and B are negligible compared to the distance of separation.

The electrostatic force on a small sphere of charge $0.4 \mu C$ due to another small sphere of charge $-0.8 \mu C$ in air is 0.2 N. (a) What is the distance between the two spheres?

A polythene piece rubbed with wool is found to have a negative charge of $3 \times 10^{-7}$ C. (b) Is there a transfer of mass from wool to polythene?

A point charge causes an electric flux of $-1.0 \times 10^3$ Nm$^2$/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (b) What is the value of the point charge?

A point charge of $2.0 \mu C$ is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?

A polythene piece rubbed with wool is found to have a negative charge of $3 \times 10^{-7}$ C. (a) Estimate the number of electrons transferred (from which to which?)

A point charge causes an electric flux of $-1.0 \times 10^3$ Nm$^2$/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?

An electric dipole with dipole moment $4 \times 10^{-9}$ C m is aligned at $30^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^4$ NC$^{-1}$. Calculate the magnitude of the torque acting on the dipole.

An infinite line charge produces a field of $9 \times 10^4$ N/C at a distance of 2 cm. Calculate the linear charge density.

Explain the meaning of the statement ‘electric charge of a body is quantised’.

Consider a uniform electric field $E = 3 \times 10^3 \hat{i}$ N/C. (b) What is the flux through the same square if the normal to its plane makes a $60^{\circ}$ angle with the x-axis?

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17.0 \times 10^{-22}$ C/m$^2$. What is $E$: (a) in the outer region of the first plate,

Consider a uniform electric field $E = 3 \times 10^3 \hat{i}$ N/C. (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane?

A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of $80.0 \mu C/m^2$. (b) What is the total electric flux leaving the surface of the sphere?

Two point charges $q_A = 3 \mu C$ and $q_B = -3 \mu C$ are located 20 cm apart in vacuum. (b) If a negative test charge of magnitude $1.5 \times 10^{-9}$ C is placed at this point, what is the force experienced by the test charge?

Figure 1.30 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

A system has two charges $q_A = 2.5 \times 10^{-7}$ C and $q_B = -2.5 \times 10^{-7}$ C located at points A: (0, 0, –15 cm) and B: (0,0, +15 cm), respectively. What are the total charge and electric dipole moment of the system?