Figure shows a charged conductor resting on an insulating stand. If at point P charge density is sig

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2. Electric Potential and Capacitance

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Figure shows a charged conductor resting on an insulating stand. If at the point $P$ the charge density is $\sigma $, the potential is $V$ and the electric field strength is $E$, what are the values of these quantities at point $Q$

Charge density potential Electric intensity

$> \sigma\,\,\,\,\,> V\,\,\,\,\,> E$

$> \sigma\,\,\,\, V\,\,\,\, > E$

$< \sigma\,\,\,\, V\,\,\,\, E$

$< \sigma\,\,\,\, V\,\,\,\, < E$

Solution

(d) The surface of the conductor is an equipotential surface since there is free flow of electrons within the conductor. Thus potential at $Q$ is the same as that at $ P$. That is ${V_P} = {V_Q} = V.$ The electric field $E$ at a point on the equipotential surface of the conductor is inversely proportional to the square of the radius of curvature $r$ at that point. That is $E \propto {r^{ – 2}}$
Since point $Q$ has a larger radius of curvature than that at point $P$, the electric field at $Q$ is less than that at $P$. That is ${E_Q} < {E_P} = E$

Standard 12

Physics

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge $Q. $

$(a)$ A charge $q$ is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

$(b)$ Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

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The magnitude of electric field on the surface of a uniformly charged metalic spherical shell is $E$. If a hole is made in it using a insulating device, then the magnitude of electric field in the hole will be

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An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in figure.If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the surface carries a uniform charge density $ '\sigma '$

If the outer surface of the shell is earthed, then identify the correct statement(s)

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If electric potential of the inner sphere is $10\, volt$ and that of the outer shell is $50\, volt$ then potential at common centre is :-……$V$

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Figure shows three concentric metallic spherical shells. The outermost shell has charge $q_2$, the inner most shell has charge $q_1$, and the middle shell is uncharged. The charge appearing on the inner surface of outermost shell is

medium

Figure shows a charged conductor resting on an insulating stand. If at the point $P$ the charge density is $\sigma $, the potential is $V$ and the electric field strength is $E$, what are the values of these quantities at point $Q$ Charge density potential Electric intensity

Solution

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The magnitude of electric field on the surface of a uniformly charged metalic spherical shell is $E$. If a hole is made in it using a insulating device, then the magnitude of electric field in the hole will be

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Figure shows a charged conductor resting on an insulating stand. If at the point $P$ the charge density is $\sigma $, the potential is $V$ and the electric field strength is $E$, what are the values of these quantities at point $Q$

Charge density potential Electric intensity