Two metal spheres, one of radius $R$ and the other of radius $2R$, both have same surface charge density $\sigma $. They are brought in contact and separated. What will be new surface charge densities on them ?
Two metal spheres, one of radius $R$ and the other of radius $2R$, both have same surface charge density $\sigma $. They are brought in contact and separated. What will be new surface charge densities on them ?
Let charges on metal spheres before contact are $\mathrm{Q}_{1}$ and $\mathrm{Q}_{2}$ hence,
$\mathrm{Q}_{1}=\sigma \times 4 \pi \mathrm{R}^{2} \text { and } \mathrm{Q}_{2}=\sigma \times 4 \pi(2 \mathrm{R})^{2} ~\\ =\sigma \times 16 \pi \mathrm{R}^{2}$ $=4 \mathrm{Q}_{1}$
Let the charges on metal sphere, after coming in contact becomes $\mathrm{Q}_{1}{ }^{\prime}$ and $\mathrm{Q}_{2}{ }^{\prime} .$
According to law of conservation of charges,
$\mathrm{Q}_{1}^{\prime}+\mathrm{Q}_{2}^{\prime}=\mathrm{Q}_{1}+\mathrm{Q}_{2}$ $=\mathrm{Q}_{1}+4 \mathrm{Q}_{1}$ $=5 \mathrm{Q}_{1}$ $=5\left(\sigma \times 4 \pi \mathrm{R}^{2}\right)$
When metal spheres come in contact they acquire equal potentials.
$\therefore \mathrm{V}_{1}=\mathrm{V}_{2}$
$\frac{k \mathrm{Q}_{1}^{\prime}}{\mathrm{R}}=\frac{k \mathrm{Q}_{2}^{\prime}}{\mathrm{R}}$
Putting value of $Q_{1}^{\prime}$ and $Q_{2}^{\prime}$ in above equations,
$\mathrm{Q}_{1}=\frac{5}{3}\left(\sigma \times 4 \pi \mathrm{R}^{2}\right)$
$text { and } \mathrm{Q}_{2}=\frac{10}{3}\left(\sigma \times 4 \pi \mathrm{R}^{2}\right)$
$\therefore \sigma_{1}=\frac{5}{3} \sigma \text { and } \sigma_{2}=\frac{5}{6} \sigma$
Similar Questions
Consider an initially neutral hollow conducting spherical shell with inner radius $r$ and outer radius $2 r$. A point charge $+Q$ is now placed inside the shell at a distance $r / 2$ from the centre. The shell is then grounded by connecting the outer surface to the earth. $P$ is an external point at a distance $2 r$ from the point charge $+Q$ on the line passing through the centre and the point charge $+Q$ as shown in the figure. The magnitude of the force on a test charge $+q$ placed at $P$ will be
Consider an initially neutral hollow conducting spherical shell with inner radius $r$ and outer radius $2 r$. A point charge $+Q$ is now placed inside the shell at a distance $r / 2$ from the centre. The shell is then grounded by connecting the outer surface to the earth. $P$ is an external point at a distance $2 r$ from the point charge $+Q$ on the line passing through the centre and the point charge $+Q$ as shown in the figure. The magnitude of the force on a test charge $+q$ placed at $P$ will be
- [KVPY 2013]
Obtain an expression for electric field at the surface of a charged conductor.
Obtain an expression for electric field at the surface of a charged conductor.
Conduction electrons are almost uniformly distributed within a conducting plate. When placed in an electrostatic field $\overrightarrow E $, the electric field within the plate
Conduction electrons are almost uniformly distributed within a conducting plate. When placed in an electrostatic field $\overrightarrow E $, the electric field within the plate
A positive point charge $q$ is placed at a distance $2 R$ from the surface of a metallic shell of radius $R$. The electric field at centre of shell due to induced charge has magnitude
A positive point charge $q$ is placed at a distance $2 R$ from the surface of a metallic shell of radius $R$. The electric field at centre of shell due to induced charge has magnitude
Two metallic spheres of radii $1\,cm$ and $2\,cm$ are given charges ${10^{ - 2}}\,C$ and $5 \times {10^{ - 2}}\,C$ respectively. If they are connected by a conducting wire, the final charge on the smaller sphere is
Two metallic spheres of radii $1\,cm$ and $2\,cm$ are given charges ${10^{ - 2}}\,C$ and $5 \times {10^{ - 2}}\,C$ respectively. If they are connected by a conducting wire, the final charge on the smaller sphere is
- [AIPMT 1995]