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Correct answer is (c) decreases K times

(d) infinite

Working : A high-voltage source, consisting of a high-voltage transformer rectifier circuit, is used to apply a potential difference of several thousand volts (about 50 kV to 100 kV) between spraycomb A and the ground. As a result of the high potential to spraycomb A, a continuous electric discharge takes place between comb A and the nonconducting belt that sprays electric charges onto the belt by corona or point discharge.

The moving belt carries this charge upward and transfers it to the hollow conductor. Collector comb B y inside the hollow conductor removes the charge from the belt by point discharge. Then, the charge flows to the outer surface of the hollow conductor where it accumulates as the process continues. The potential difference between the conductor and the Earth cumulatively increases until the energy density of the electric field builds up to such a high value that the insulating property of the surrounding gas breaks down and a corona discharge takes place through the surrounding gas between the conductor and the ground. If C is the capacitance of – the system and |Q| is the magnitude of the charge transferred from the ground to the conductor, the potential difference V between them is given by V = |Q|/C.

If the hollow conductor is well insulated from the Earth, the accumulated charge |Q| can be large enough and V can build up to several million volts. Since V is limited by the breakdown voltage of the surrounding medium, the entire apparatus is usually enclosed in a pressurized vessel containing a gas such as nitrogen or Freon. This raises the breakdown voltage considerably

Positively charged particles may be accelerated in the evacuated tube from a source at the same potential as the dome conductor toward a target at the ground potential.

Uses : Machines equipped with positive ion sources and arranged for positive ion acceleration are widely used for research in nuclear structure and nuclear reactions, and for production of radioisotopes. Machines equipped with electron sources are used for X-ray therapy, industrial radiography, food and drug sterilization as well as research.

[Note : in a Van de Graaff single-stage accelerator, an ion source is located inside the high-voltage terminal (the dome conductor). Since the electric field inside a charged conductor is zero, the source must be at the same potential as the terminal. The ions are accelerated to the target (at the ground potential) by repulsion. Early quan-titative data on nuclear properties and processes came from Van de Graaff positive ion accelerators, which had a positive ion (proton, deuteron, alpha particle) source and the high voltage terminal raised to a high positive potential. Van de Graaff electron accelerators had also been very successful as sources for X-rays for radiotherapy and industrial radiography. For an electrostatic electron accel-erator, the terminal is charged to a high negative potential and a thermionic cathode replaces the ion source. Accel-erated electrons impinging on watercooled gold targets provided for the first time high energy X-rays (~2 MeV) for cancer therapy. A number of such X-ray generators were developed by Prof. J. G. Trump and R.J. Van de Graaff which were installed in hospitals and industries. These instruments were about 3 ft in diameter and 6 ft long, and could be swung into any position to direct the X-ray beam.]

Correct answer is  (a) K : 1

Charge produced in each object q = 50 nC 

q = 50 x 10^-9 C 

Charge of electron (e) = 1.6 x 10^-9 C 

Number of electron transferred, n = \(\frac {q}{e}\) = \(\frac {50 \times 10^{-9}}{1.6 \times 10^{-19}}\) 

=31. 25 × 10^-9 × 10¹⁹ 

n = 31.25 x 10¹⁰ 

electrons 

Ans. n = 31.25 x 10¹⁰ electrons

A non-polar molecule is one in which centers of positive and negative charges coincide. As a result, it has no permanent dipole moment. 

Examples of non-polar molecules are hydrogen (H₂ ), oxygen (O₂ ), and carbon dioxide (CO₂ ) etc.

Polarisation is defined as the total dipole moment per unit volume of the dielectric.

\(\vec P\)= X_e \(\vec P\)_ext

A dielectric is a non-conducting material and has no free electrons. The electrons in a dielectric are bound within the atoms. Ebonite, glass and mica are some examples of dielectrics.

Consider a cavity inside the conductor. Whatever the charges at the surfaces and whatever the electrical disturbances outside, the electric field inside the cavity is zero. A sensitive electrical instrument which is to be  protected from external electrical disturbance is kept inside this cavity. This is called electrostatic shielding.

The energy stored per unit volume of space is defined as energy density

u_E = \(\frac{U}{Volume}\)

From equation u_E = 1/2 \(\frac {ε_0A}{d}\)(Ed)² = 1/2 ε₀ (Ad)E²  

or u_E = 1/2 ε₀ E²

During lightning accompanied by a thunderstorm, it is always safer to sit inside a bus than in open ground or under a tree. The metal body of the bus provides electrostatic shielding, since the electric field inside is zero. During lightning, the charges flow through the body of the conductor to the ground with no effect on the person inside that bus.

Van de Graaff generator producers large electrostatic potential difference of the order of 10⁷ V

(i) → (c) 

(ii) → (d)

(iii) → (a) 

(iv) → (b)

C = = 0.05 nF = 50 pF

From the graph, for Q = 0.5 nC, ∆V = 10 V.