(C) Initially,the force between the two spheres is given by Coulomb's Law: $F = k \frac{|q_1 q_2|}{r^2} = k \frac{|(+8 \mu C)(-4 \mu C)|}{r^2} = k \fr

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(C) Initially,the force between the two spheres is given by Coulomb's Law: $F = k \frac{|q_1 q_2|}{r^2} = k \frac{|(+8 \mu C)(-4 \mu C)|}{r^2} = k \frac{32 \mu C^2}{r^2}$.When the two identical conducting spheres are connected by a wire,the charges redistribute equally because they have the same radius.The new charge on each sphere will be $q' = \frac{q_1 + q_2}{2} = \frac{+8 \mu C - 4 \mu C}{2} = +2 \mu C$.The new force $F'$ between the spheres is $F' = k \frac{|q' q'|}{r^2} = k \frac{|(+2 \mu C)(+2 \mu C)|}{r^2} = k \frac{4 \mu C^2}{r^2}$.Comparing the two forces: $\frac{F'}{F} = \frac{4}{32} = \frac{1}{8}$.Therefore,$F' = \frac{F}{8}$.

Class 12 Physics Electric Charges and Fields Mix Examples-Electric Charges and Fields

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The force between two conducting spheres of same radius having charges $+8 \mu C$ and $-4 \mu C$ separated by some distance in air is $F$. If the spheres are connected by a conducting wire and after some time the wire is removed,then the magnitude of the force between the two conducting spheres is

AP EAMCET 2025 All AP EAMCET

A
$F$
B
$F/2$
C
$F/8$
D
$F/4$

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Electric Charges and Fields

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Mix Examples-Electric Charges and Fields

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Five balls marked $a$ to $e$ are suspended using separate threads. Pairs $(b, c)$ and $(d, e)$ show electrostatic repulsion,while pairs $(a, b)$,$(c, e)$,and $(a, e)$ show electrostatic attraction. The ball marked $a$ must be:

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Two charges,each equal to $q$,are kept at $x = -a$ and $x = a$ on the $x$-axis. $A$ particle of mass $m$ and charge $q_0 = \frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $(y << a)$ along the $y$-axis,the net force acting on the particle is proportional to

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$A$ thin spherical insulating shell of radius $R$ carries a uniformly distributed charge such that the potential at its surface is $V_0$. $A$ hole with a small area $\alpha 4 \pi R^2$ (where $\alpha \ll 1$) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

IIT 2019

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How much work is done in moving a charge $+q$ once around a circle of radius $r$ in the presence of a central charge $+Q$?

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Column $II$ corresponds to the graph of magnitude of electric field versus distance from the centre of the charge distribution in Column $I$. Match the items in Column $I$ with the corresponding graphs in Column $II$.

Column-$I$ Column-$II$

$(A)$ Ring along its axis $(P)$ Graph with a peak at a distance $r > 0$

$(B)$ Uniformly charged solid sphere $(Q)$ Graph increasing linearly for $r < R$ and decreasing as $1/r^2$ for $r > R$

$(C)$ Uniformly charged spherical shell $(R)$ Graph with zero field for $r < R$ and decreasing as $1/r^2$ for $r > R$

$(D)$ Combination of charge $+Q$ and $-Q$ at the perpendicular bisector $(S)$ Graph with a maximum at the center and decreasing as $r$ increases

Column-$I$	Column-$II$
$(A)$ Ring along its axis	$(P)$ Graph with a peak at a distance $r > 0$
$(B)$ Uniformly charged solid sphere	$(Q)$ Graph increasing linearly for $r < R$ and decreasing as $1/r^2$ for $r > R$
$(C)$ Uniformly charged spherical shell	$(R)$ Graph with zero field for $r < R$ and decreasing as $1/r^2$ for $r > R$
$(D)$ Combination of charge $+Q$ and $-Q$ at the perpendicular bisector	$(S)$ Graph with a maximum at the center and decreasing as $r$ increases

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The force between two conducting spheres of same radius having charges $+8 \mu C$ and $-4 \mu C$ separated by some distance in air is $F$. If the spheres are connected by a conducting wire and after some time the wire is removed,then the magnitude of the force between the two conducting spheres is

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Five balls marked $a$ to $e$ are suspended using separate threads. Pairs $(b, c)$ and $(d, e)$ show electrostatic repulsion,while pairs $(a, b)$,$(c, e)$,and $(a, e)$ show electrostatic attraction. The ball marked $a$ must be:

Two charges,each equal to $q$,are kept at $x = -a$ and $x = a$ on the $x$-axis. $A$ particle of mass $m$ and charge $q_0 = \frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $(y << a)$ along the $y$-axis,the net force acting on the particle is proportional to

How much work is done in moving a charge $+q$ once around a circle of radius $r$ in the presence of a central charge $+Q$?

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