Question 18

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.)

Answer

The square can be considered as one face of a cube of edge 10 cm with a centre where charge q is placed. According to Gauss’s theorem for a cube, total electric flux is through all its six faces.

Hence, electric flux through one face of the cube i.e., through the square,

Where, ∈0 = Permittivity of free space

= 8.854 × 10^{−12} N^{−1}C^{2} m^{−2} q = 10 μC = 10 × 10^{−6} C

∴

= 1.88 × 10^{5} N m^{2} C^{−1}

Therefore, electric flux through the square is 1.88 × 10^{5} N m^{2} C^{−1}.

- Q:- A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.

(a) What is the rms value of current in the circuit?

(b) What is the net power consumed over a full cycle? - 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:-
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:- The work function of caesium metal is 2.14 eV. When light of frequency 6 ×10
^{14}Hz is incident on the metal surface, photoemission of electrons occurs. What is the(a) maximum kinetic energy of the emitted electrons,

(b) Stopping potential, and

(c) maximum speed of the emitted photoelectrons?

">The work function of caesium metal is 2.14 eV. When light of frequency 6 ×10

^{14}Hz is incident on the metal surface, photoemission of electrons occurs. What is the(a) maximum kinetic energy of the emitted electrons,

(b) Stopping potential, and

(c) maximum speed of the emitted photoelectrons?

- Q:-
Consider a uniform electric field E = 3 × 10

^{3}îN/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?

(b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?

- 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:-
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:-
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 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:-
Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of

(a) reflected, and

(b) refracted light? Refractive index of water is 1.33.

- 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:-
A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

- Q:-
A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q.

(a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

- Q:- (a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.
(b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

">(a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.

(b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

- Q:-
A system has two charges q

_{A}= 2.5 × 10^{−7}C and q_{B}= −2.5 × 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? - Q:- The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of charge − 0.8 μC in air is 0.2 N.
(a) What is the distance between the two spheres?

(b) What is the force on the second sphere due to the first?

">The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of charge − 0.8 μC in air is 0.2 N.

(a) What is the distance between the two spheres?

(b) What is the force on the second sphere due to the first?

- 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:-
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 × 10

^{−22}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?

- Q:-
(a) Two insulated charged copper spheres A and B have their centers separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 × 10

^{−7}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?

- Q:-
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?

Anamika
2019-11-24 15:34:39

Thnq ð

Pratisha
2019-06-18 22:30:02

Can we solve this without using Gauss law?? ( By using EdScos0 alone)

Arvendra dhakar
2018-12-25 07:29:22

Thanks a lot

Shivangi srivastava
2018-07-01 12:04:54

Thanks

Miracle
2017-06-16 13:41:37

Two charges q1= 10uc and q2= -12uc are within a spherical surface of radius 10cm. What is the total flux through the surface ?

Harsh
2017-04-22 13:09:50

Nice

Student
2017-04-16 11:13:19

Thanks a lot

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