Question 27

In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 105 NC^{-1 }per metre. What are the force and torque experienced by a system having a total dipole moment equal to 10^{-7} Cm in the negative z-direction?

Answer

Dipole moment of the system, p = q × dl = −10^{−7} C m

Rate of increase of electric field per unit length,

Force (F) experienced by the system is given by the relation,

F = qE

= −10^{−7} × 10^{−5}

= −10^{−2} N

The force is −10^{−2} N in the negative z-direction i.e., opposite to the direction of electric field. Hence, the angle between electric field and dipole moment is 180°.

Torque (τ) is given by the relation,

τ = pE sin180° = 0

Therefore, the torque experienced by the system is zero.

- Q:-
An infinite line charge produces a field of 9 × 10

^{4}N/C at a distance of 2 cm. Calculate the linear charge density. - Q:-
What is the force between two small charged spheres having charges of 2 x 10

^{-7}C and 3 x 10^{-7}C placed 30 cm apart in air? - Q:-
A polythene piece rubbed with wool is found to have a negative charge of 3 × 10

^{−7}C.(a) Estimate the number of electrons transferred (from which to which?)

(b) Is there a transfer of mass from wool to polythene?

- Q:-
A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?

- Q:-
A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10

^{-12}F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6? - Q:- A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?
- Q:-
A regular hexagon of side 10 cm has a charge 5 µC at each of its vertices. Calculate the potential at the centre of the hexagon.

- Q:-
A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 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 cm.)

- Q:-
A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?

- Q:-
A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 × 10

^{3}N/C and points radially inward, what is the net charge on the sphere?

- Q:-
What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30º with the direction of a uniform magnetic field of 0.15 T?

- Q:-
Two point charges q

_{A}= 3 μC and q_{B}= −3 μC are located 20 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 × 10

^{−9}C is placed at this point, what is the force experienced by the test charge? - Q:-
Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).

- Q:-
A regular hexagon of side 10 cm has a charge 5 µC at each of its vertices. Calculate the potential at the centre of the hexagon.

- Q:-
What is the Brewster angle for air to glass transition? (Refractive index of glass = 1.5.)

- Q:-
Obtain the formula for the electric field due to a long thin wire of uniform linear charge density λ without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary integral.]

- Q:-
A short bar magnet of magnetic moment 5.25 x 10

^{-2}J T^{-1}is placed with its axis perpendicular to the earth's field direction. At what distance from the centre of the magnet, the resultant field is inclined at 45º with earth's field on(a) its normal bisector and (b) its axis. Magnitude of the earth's field at the place is given to be 0.42 G. Ignore the length of the magnet in comparison to the distances involved.

- Q:-
**(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? - Q:-
A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?

- Q:-
A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?

Sanu
2019-05-19 22:04:10

Thanks

Ekamjeet Singh Grewal
2018-11-03 14:49:39

There's a error in the typing

- NCERT Chapter

Copyright © 2021 saralstudy.com. All Rights Reserved.