(B) For a point at a distance $r$ such that $R_1 < r < R_2$,the potential $V$ is the sum of the potentials due to both spheres.$1$. The potential due

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$\frac{1}{4\pi \varepsilon_0} \left( \frac{Q_1}{r} + \frac{Q_2}{R_2} \right)$

(B) For a point at a distance $r$ such that $R_1 $1$. The potential due to the inner sphere (radius $R_1$,charge $Q_1$) at a distance $r$ (where $r > R_1$) is $V_1 = \frac{1}{4\pi \varepsilon_0} \frac{Q_1}{r}$.$2$. The potential due to the outer sphere (radius $R_2$,charge $Q_2$) at a distance $r$ (where $r $3$. The total potential $V$ at distance $r$ is $V = V_1 + V_2 = \frac{1}{4\pi \varepsilon_0} \left( \frac{Q_1}{r} + \frac{Q_2}{R_2} \right)$.

Class 12 Physics Electric Potential and Capacitance Electric potential

Medium

Two thin concentric hollow conducting spheres of radii $R_1$ and $R_2$ bear charges $Q_1$ and $Q_2$ respectively. If $R_1 < R_2$,then the potential of a point at a distance $r$ from the centre $(R_1 < r < R_2)$ is

A
$\frac{1}{4\pi \varepsilon_0} \left( \frac{Q_1 + Q_2}{r} \right)$
B
$\frac{1}{4\pi \varepsilon_0} \left( \frac{Q_1}{r} + \frac{Q_2}{R_2} \right)$
C
$\frac{1}{4\pi \varepsilon_0} \left( \frac{Q_1}{R_1} + \frac{Q_2}{R_2} \right)$
D
$\frac{1}{4\pi \varepsilon_0} \left( \frac{Q_1}{R_1} + \frac{Q_2}{r} \right)$

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Class 12

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Electric Potential and Capacitance

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Electric potential

$125$ identical charged small spheres coalesce to form a big charged sphere. If the electric potential on each small sphere is $60 \text{ mV}$, then the electric potential on the bigger sphere formed is: (in $\text{ V}$)

MediumAP EAMCET 2024

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Electric charges having the same magnitude $q$ are placed at $x = 1 \, m, 2 \, m, 4 \, m, 8 \, m, \dots$ and so on. If any two consecutive charges have opposite signs but the first charge is necessarily positive,what will be the potential at $x = 0$?

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$(a)$ Calculate the potential at a point $P$ due to a charge of $4 \times 10^{-7} \; C$ located $9 \; cm$ away.
$(b)$ Hence,obtain the work done in bringing a charge of $2 \times 10^{-9} \; C$ from infinity to the point $P$. Does the answer depend on the path along which the charge is brought?

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$A$ charge $Q$ is distributed over two concentric conducting thin spherical shells of radii $r$ and $R$ $(R > r)$. If the surface charge densities on the two shells are equal,the electric potential at the common centre is

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Calculate the work done in taking a charge $q_0 = -2 \times 10^{-9} \, C$ from point $A$ to point $B$ via point $C$,as shown in the diagram. The source charge $q = 8 \, mC$ is located at the origin $O$. (in $, J$)

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Two thin concentric hollow conducting spheres of radii $R_1$ and $R_2$ bear charges $Q_1$ and $Q_2$ respectively. If $R_1 < R_2$,then the potential of a point at a distance $r$ from the centre $(R_1 < r < R_2)$ is

Similar Questions

$125$ identical charged small spheres coalesce to form a big charged sphere. If the electric potential on each small sphere is $60 \text{ mV}$, then the electric potential on the bigger sphere formed is: (in $\text{ V}$)

Electric charges having the same magnitude $q$ are placed at $x = 1 \, m, 2 \, m, 4 \, m, 8 \, m, \dots$ and so on. If any two consecutive charges have opposite signs but the first charge is necessarily positive,what will be the potential at $x = 0$?

$(a)$ Calculate the potential at a point $P$ due to a charge of $4 \times 10^{-7} \; C$ located $9 \; cm$ away.$(b)$ Hence,obtain the work done in bringing a charge of $2 \times 10^{-9} \; C$ from infinity to the point $P$. Does the answer depend on the path along which the charge is brought?

$A$ charge $Q$ is distributed over two concentric conducting thin spherical shells of radii $r$ and $R$ $(R > r)$. If the surface charge densities on the two shells are equal,the electric potential at the common centre is

Calculate the work done in taking a charge $q_0 = -2 \times 10^{-9} \, C$ from point $A$ to point $B$ via point $C$,as shown in the diagram. The source charge $q = 8 \, mC$ is located at the origin $O$. (in $, J$)

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$(a)$ Calculate the potential at a point $P$ due to a charge of $4 \times 10^{-7} \; C$ located $9 \; cm$ away.
$(b)$ Hence,obtain the work done in bringing a charge of $2 \times 10^{-9} \; C$ from infinity to the point $P$. Does the answer depend on the path along which the charge is brought?