Welcome to the NCERT Solutions for Class 12th Physics - Chapter Electric Charges and Field. This page offers a step-by-step solution to the specific question from Exercise 1, Question 22: **a uniformly charged conducting sphere of 2 4 m dia...**.

Question 22

A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC/m^{2}.

(a) Find the charge on the sphere.

(b) What is the total electric flux leaving the surface of the sphere?

Answer

(a) Diameter of the sphere, d = 2.4 m

Radius of the sphere, r = 1.2 m

Surface charge density, = 80.0 μC/m2 = 80 × 10−6 C/m2

Total charge on the surface of the sphere,

Q = Charge density × Surface area

=

= 80 × 10^{−6} × 4 × 3.14 × (1.2)^{2}

= 1.447 × 10^{−3} C

Therefore, the charge on the sphere is 1.447 × 10^{−3} C.

(b) Total electric flux () leaving out the surface of a sphere containing net charge Q is given by the relation,

Where, ∈0 = Permittivity of free space

∈_{0} = 8.854 × 10^{−12} N^{−1}C^{2} m^{−2}

Q = 1.447 × 10^{−3} C

= 1.63 × 10^{8} N C^{−1} m^{2}

Therefore, the total electric flux leaving the surface of the sphere is 1.63 × 10^{8} N C^{−1} m^{2}.

- 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 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 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 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:-
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:-
An electric dipole with dipole moment 4 × 10

^{−9}C m is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 10^{4}N C^{−1}. Calculate the magnitude of the torque acting on the dipole. - 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?

- Q:-
Answer the following questions regarding earth's magnetism:

(a) A vector needs three quantities for its specification. Name the three independent quantities conventionally used to specify the earth's magnetic field.

(b) The angle of dip at a location in southern India is about 18º.

Would you expect a greater or smaller dip angle in Britain?

(c) If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground?

(d) In which direction would a compass free to move in the vertical plane point to, if located right on the geomagnetic north or south pole?

(e) The earth's field, it is claimed, roughly approximates the field due to a dipole of magnetic moment 8 x 1022 J T

^{-1 }located at its centre. Check the order of magnitude of this number in some way.(f ) Geologists claim that besides the main magnetic N-S poles, there are several local poles on the earth's surface oriented in different directions. How is such a thing possible at all?

- Q:-
(a) Two stable isotopes of lithium 6Li3 and7Li3 have respective abundances of 7.5% and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u, respectively. Find the atomic mass of lithium.

(b) Boron has two stable isotopes,

^{10}B_{5}and^{11}B_{5}. Their respective masses are 10.01294 u and 11.00931 u, and the atomic mass of boron is 10.811 u. Find the abundances of^{10}B_{5}and^{11}B_{5}. - Q:-
A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

- Q:-
Figure 8.6 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A.

(a) Calculate the capacitance and the rate of charge of potential difference between the plates.

(b) Obtain the displacement current across the plates.

(c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

- Q:- The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4Ω, what is the maximum current that can be drawn from the battery?
- 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 rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s−1 in a direction normal to the

(a) longer side,

(b) shorter side of the loop? For how long does the induced voltage last in each case? - 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:-
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:-
Two charges 5 x 10

^{-8}C and -3 x 10^{-8}C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

- Q:-
A spherical conductor of radius 12 cm has a charge of 1.6 x 10

^{-7}C distributed uniformly on its surface. What is the electric field(a) Inside the sphere

(b) Just outside the sphere

(c) At a point 18 cm from the centre of the sphere?

- Q:-
A magnetic field of 100 G (1 G = 10

^{-4}T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10^{-3}m^{2}. The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m^{-1}. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic - 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:-
Two charges 5 x 10

^{-8}C and -3 x 10^{-8}C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero. - 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:-
In a Young’s double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

- Q:-
Answer the following questions:

(a) The earths magnetic field varies from point to point in space. Does it also change with time? If so, on what time scale does it change appreciably?

(b) The earths core is known to contain iron. Yet geologists do not regard this as a source of the earths magnetism. Why?

(c) The charged currents in the outer conducting regions of the earths core are thought to be responsible for earths magnetism. What might be the battery (i.e., the source of energy) to sustain these currents?

(d) The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earths field in such distant past?

(e) The earths field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

(f ) Interstellar space has an extremely weak magnetic field of the order of 10−12 T. Can such a weak field be of any significant consequence? Explain.

[Note: Exercise 5.2 is meant mainly to arouse your curiosity. Answers to some questions above are tentative or unknown. Brief answers wherever possible are given at the end. For details, you should consult a good text on geomagnetism.] - Q:-
A 4 µF capacitor is charged by a 200 V supply. It is then disconnected from the supply, and is connected to another uncharged 2 µF capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

- Q:-
Two towers on top of two hills are 40 km apart. The line joining them passes 50 m above a hill halfway between the towers. What is the longest wavelength of radio waves, which can be sent between the towers without appreciable diffraction effects?

- Q:-
A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?

Steven
2019-11-24 07:32:59

Thank you it was really useful

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