A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 µC. The space between the concentric spheres is filled with a liquid of dielectric constant 32.
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.
Radius of the inner sphere, r2 = 12 cm = 0.12 m
Radius of the outer sphere, r1= 13 cm = 0.13 m
Charge on the inner sphere, q = 2.5 μC = 2.5 x 10-6 C
Dielectric constant of a liquid, ∈r = 32
(a) Capacitance of the capacitor is given by the relation,
Where,
∈0 = Permittivity of free space = 8.85 x 10-12 C2 N-1 m-2
Hence, the capacitance of the capacitor is approximately 5.5 x 10-9 F.
(b) Potential of the inner sphere is given by,
Hence, the potential of the inner sphere is 4.5 x 102 V.
(c) Radius of an isolated sphere, r = 12 x 10-2 m
Capacitance of the sphere is given by the relation,
The capacitance of the isolated sphere is less in comparison to the concentric spheres. This is because the outer sphere of the concentric spheres is earthed. Hence, the potential difference is less and the capacitance is more than the isolated sphere.
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(a) Estimate the number of electrons transferred (from which to which?)
(b) Is there a transfer of mass from wool to polythene?
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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 × 103 N/C and points radially inward, what is the net charge on the sphere?
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?
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 × 104N C−1. Calculate the magnitude of the torque acting on the dipole.
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(a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm.
(b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?
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(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?
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(a) Find the charge on the sphere.
(b) What is the total electric flux leaving the surface of the sphere?
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(b) What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?
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(b) total force on the coil,
(c) average force on each electron in the coil due to the magnetic field?
(The coil is made of copper wire of cross-sectional area 10-5 m2, and the free electron density in copper is given to be about 1029 m-3.)
sir define brief about the potential diffrence how it is less for concentric spheres
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