List of practice Questions

Scheme A offers 25% interest and scheme B offers 20% interest. M invested Rs.4000 in scheme A and Rs.6000 in scheme B at compound interest. After 2 years, he invested the amount received from scheme A and B in schemes B and A respectively at simple interest for 2 more years. If another person N invested Rs.6000 in scheme A and Rs.4000 in scheme B at compound interest. After 2 years, he invested the amount received from scheme A and B in schemes B and A respectively at simple interest for 2 more years, then what is the difference between total amount received by M and N after 4 years?

A metal ring is held horizontally and bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is

A black body at $227^{\circ} C$ radiates heat at the rate of $7\, cals / cm ^{2} s$. At a temperature of $727^{\circ} C$, the rate of heat radiated in the same units will be :

Figure 2.11shows the x-t plot of one dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for t < 0 and on a parabolic path for t >0 ? If not, suggest a suitable physical context for this graph.

A given metal crystallizes out with a cubic structure having edge length of 361 pm. If there are four metal aotms in one unit cell, what is the radius of one atom?

A point charge $+10\,\mu\text{C}$ is a distance $5\,\text{cm}$ directly above the centre of a square of side $10\,\text{cm}$, as shown in Fig. 1.34. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge $10\,\text{cm}$.)

Figure 1.33 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?

An infinite line charge produces a field of $9\times10^{4}\,\text{N/C}$ at a distance of $2\,\text{cm}$. Calculate the linear charge density.

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 $17.0\times10^{-22}\,\text{C/m}^{2}$. What is $E$: (a) in the outer region of the first plate, (b) in the outer region of the second plate, and (c) between the plates?

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

A point charge causes an electric flux of $-1.0\times10^{3}\,\text{N m}^{2}/\text{C}$ to pass through a spherical Gaussian surface of $10.0\,\text{cm}$ radius centred on the charge.
(a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?
(b) What is the value of the point charge?

A conducting sphere of radius $10\,\text{cm}$ has an unknown charge. If the electric field $20\,\text{cm}$ from the centre of the sphere is $1.5\times10^{3}\,\text{N/C}$ and points radially inward, what is the net charge on the sphere?

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

(a) Two insulated charged copper spheres A and B have their centres separated by a distance of $50\,\text{cm}$. What is the mutual force of electrostatic repulsion if the charge on each is $6.5\times10^{-7}\,\text{C}$? The radii of A and B are negligible compared to the distance of separation.
(b) What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?

Suppose the spheres A and B in Exercise 1.12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B?

Consider a uniform electric field $\vec E = 3\times10^{3}\,\hat\imath\,\text{N/C}$.
(a) What is the flux of this field through a square of $10\,\text{cm}$ on a side whose plane is parallel to the $yz$-plane?
(b) What is the flux through the same square if the normal to its plane makes a $60°$ angle with the $x$-axis?

What is the net flux of the uniform electric field of Exercise 1.15 through a cube of side $20\,\text{cm}$ oriented so that its faces are parallel to the coordinate planes?

Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is $8.0\times10^{3}\,\text{N m}^{2}/\text{C}$.
(a) What is the net charge inside the box?
(b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or why not?

Four point charges $q_A = 2\,\mu\text{C}$, $q_B = -5\,\mu\text{C}$, $q_C = 2\,\mu\text{C}$, $q_D = -5\,\mu\text{C}$ are located at the corners of a square ABCD of side $10\,\text{cm}$. What is the force on a charge of $1\,\mu\text{C}$ placed at the centre of the square?

(a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
(b) Explain why two field lines never cross each other at any point.

Two point charges $q_A = 3\,\mu\text{C}$ and $q_B = -3\,\mu\text{C}$ are located $20\,\text{cm}$ apart in vacuum.
(a) What is the electric field at the midpoint O of the line AB joining the two charges?
(b) If a negative test charge of magnitude $1.5\times10^{-9}\,\text{C}$ is placed at this point, what is the force experienced by the test charge?

A system has two charges $q_A = 2.5\times10^{-7}\,\text{C}$ and $q_B = -2.5\times10^{-7}\,\text{C}$ located at points $A:(0,\,0,\,-15\,\text{cm})$ and $B:(0,\,0,\,+15\,\text{cm})$, respectively. What are the (a) total charge and (b) electric dipole moment of the system?

An electric dipole with dipole moment $4\times10^{-9}\,\text{C m}$ is aligned at $30°$ with the direction of a uniform electric field of magnitude $5\times10^{4}\,\text{N C}^{-1}$. Calculate the magnitude of the torque acting on the dipole.

A polythene piece rubbed with wool is found to have a negative charge of $3\times10^{-7}\,\text{C}$.
(a) Estimate the number of electrons transferred (from which to which?).
(b) Is there a transfer of mass from wool to polythene?

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