Question 2.31: Answer carefully: (a) Two large conducting spheres carrying charges Q1 and Q2 are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q1 Q2/4πr 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).
Class 12 - Physics - Electrostatic Potential And Capacitance Electrostatic Potential And Capacitance Page-91
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(a) No,because coulombs law hold good only for point charges .
(b) No, because in that case electric flux linked with the closed surface will also become dependent on 'r' other than enclosed by it .
(c) No, it will travel along the field line only if it is a straight line.
(d) zero, this is because work done in moving a charge in a closed path in electric field is zero as electric field is conservative.
no matter the shape of orbit , if orbit is elliptical , then also charge moves on closed path, so work done must be zero.
e.g.,
(e) No, electric potential is continuous there. As E = 0 , so dV/dr = 0 so, V = constant.
(f) it means that a single conductor is a capacitor whose other plate can be considered to be at infinity .
(g) A water molecule is a polar molecule with non-zero electric dipole moment, however mica doesn't have polar molecule.so, dielectric constant of water is high.
(b) No, because in that case electric flux linked with the closed surface will also become dependent on 'r' other than enclosed by it .
(c) No, it will travel along the field line only if it is a straight line.
(d) zero, this is because work done in moving a charge in a closed path in electric field is zero as electric field is conservative.
no matter the shape of orbit , if orbit is elliptical , then also charge moves on closed path, so work done must be zero.
e.g.,
(e) No, electric potential is continuous there. As E = 0 , so dV/dr = 0 so, V = constant.
(f) it means that a single conductor is a capacitor whose other plate can be considered to be at infinity .
(g) A water molecule is a polar molecule with non-zero electric dipole moment, however mica doesn't have polar molecule.so, dielectric constant of water is high.
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- I hope this answer is sufficient sorry for the bad handwriting
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