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:-
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:-
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:- 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 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 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 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 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:-
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 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 p-n photodiode is fabricated from a semiconductor with band gap of 2.8 eV. Can it detect a wavelength of 6000 nm?

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

- Q:-
Two tiny spheres carrying charges 1.5 μC and 2.5 μC are located 30 cm apart. Find the potential and electric field:

(a) at the mid-point of the line joining the two charges, and

(b) at a point 10 cm from this midpoint in a plane normal to the line and passing through the mid-point.

- 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:-
Answer carefully:

(a) Two large conducting spheres carrying charges Q

_{1}and Q_{2}are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q_{1}Q_{2}/4π∈_{0}r^{2}, where r is the distance between their centres?(b) If Coulomb's law involved 1/r

^{3}dependence (instead of 1/r^{2}), would Gauss's law be still true?(c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?

(d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical?

(e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?

(f) What meaning would you give to the capacitance of a single conductor?

(g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

- Q:-
What is the shape of the wavefront in each of the following cases:

(a) Light diverging from a point source.

(b) Light emerging out of a convex lens when a point source is placed at its focus.

(c) The portion of the wavefront of light from a distant star intercepted by the Earth.

- Q:- What physical quantity is the same for X-rays of wavelength 10−10 m, red light of wavelength 6800 A and radiowaves of wavelength 500 m?
- Q:-
In double-slit experiment using light of wavelength 600 nm, the angular width of a fringe formed on a distant screen is 0.1

^{o}. What is the spacing between the two slits? - Q:-
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?

Karisa
2021-12-13 01:11:42

Nice ð

SPBhagyam
2020-07-30 20:28:32

Thakzzz

SPBhagyam
2020-07-30 20:27:56

Gud

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

- NCERT Chapter