Two equally charged spheres of radii a and bare connected together. What will be the ratio of electric field intensity on their surfaces?

^a⁄_b
^a²⁄_b²
^b⁄_a
^b²⁄_a²

Solution

A charge +q is fixed at each of the points x = x₀, x = 3x₀,x = 5x₀, …. upto ∞ on X-axis and charge –q is fixed on each of the points x= 2x₀, x= 4x₀, x= 6x₀, …. upto ∞. Here x₀ is a positive constant. Take the potential at a point due to a charge Q at a distance r from it to be \(\frac{Q}{4\pi \varepsilon _{0}r}\). Then the potential at the origin due to above system of charges will be

zero
\(\frac{q}{8\pi \varepsilon _{0}x_{0}log_{e}2}\)
infinity
\(\frac{q\, log_{e}\, 2}{4\pi \varepsilon _{0}x_{0}}\)

Solution

Identical charges – q each are placed at 8 corners of a cube of each side b. Electrostatic potential energy of a charge+ q which is placed at the centre of cube will be

\(\frac{-4\sqrt{2}q^{2}}{\pi \varepsilon _{0}b}\)
\(\frac{-8\sqrt{2}q^{2}}{\pi \varepsilon _{0}b}\)
\(\frac{-4\sqrt{2}q^{2}}{\sqrt{3}\pi \varepsilon _{0}b}\)
\(\frac{-8\sqrt{2}q^{2}}{\pi \varepsilon _{0}b}\)

Solution

Two metal pieces having a potential difference of 800 V are 0.02 m apart horizontally. A particle of mass 1.96 × 10–15 kg is suspended in equilibrium between the plates. If e is the elementary charge, then charge on the particle is

Solution

A large insulated sphere of radius r charged with Q units of electricity is placed in contact with a small insulated uncharged sphere of radius r´ and is then separated. The charge on smaller sphere will now ber

Q(r'+ r)
Q(r + r')
\(\frac{Q}{r'+r}\)
\(\frac{Qr'}{r'+r}\)

Solution

he potential at a point x (measured in mm) due to some charges situated on the x-axis is given by V(x) = 20/(x2– 4)volt The electric field E at x =4 mm is given by

(10/9) volt/mm and in the +ve x direction
(5/3) volt/mm and in the –ve x direction
(5/3) volt/mm and in the +ve x direction
(10/9) volt/mm and in the –ve x direction

Solution

Two capacitors of capacitance C are connected in series. If one of them is filled with dielectric substance k, what is the effective capacitance ?

\(\frac{KC}{ \left ( 1+K \right )}\)
C(k + 1)
\(\frac{2KC}{1+K}\)
None of these

Two capacitors C₁ and C₂ = 2C₁ are connected in a circuit with a switch between them as shown in the figure. Initially the switch is open and C₁ holds charge Q. The switch is closed. At steady state, the charge on each capacitor will be

Q, 2Q
^Q⁄₃,^2Q⁄₃
^3Q⁄₂,3Q
^2Q⁄₃,^4Q⁄₃

Solution

Two capacitors, C₁= 2μF and C₂= 8 mF are connected inseries across a 300 V source. Then

the charge on each capacitor is 4.8 × 10^–4 C
the potential difference across C₁ is 60 V
the potential difference across C₂ is 240 V
the energy stroed in the system is 5.2 × 10^-2 J

Solution

A system of two parallel plates, each of area A, are separated by distances d₁ and d₂. The space between them is filled with dielectrics of permittivities ε₁ and ε₂. The permittivity of free space is ε₀. The equivalent capacitance of the system is

\(\frac{\varepsilon _{1}\varepsilon _{2}A}{\varepsilon _{2}d_{1}+\varepsilon _{1}d_{2}}\)
\(\frac{\varepsilon _{1}\varepsilon _{2}\varepsilon _{0}A}{\varepsilon _{1}d_{1}+\varepsilon _{2}d_{2}}\)
\(\frac{\varepsilon _{0}A}{\varepsilon _{1}d_{1}+\varepsilon _{2}d_{2}}\)
\(\frac{\varepsilon _{0}A}{\varepsilon _{1}d_{2}+\varepsilon _{2}d_{1}}\)

Solution

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