B M Sharma Solutions for Chapter: Electric Potential, Exercise 6: Exercise

Two small spheres are attached to the ends of a long light nonconducting rod at a distance $40 \mathrm{mm}$ from each other. A third, middle sphere can slide along the rod without friction as shown. All three spheres are nonconducting, have identical masses $m=1 \mathrm{g},$ and a positive charge $q=1 \mathrm{C}$ is distributed evenly on the surface of each sphere. The whole system is placed on a horizontal frictionless nonconducting surface. Initially, all three spheres are at rest and the middle sphere is located a distance $30 \mathrm{mm}$ from one of the ends of the rod and a distance $10 \mathrm{mm}$ from the other. Find the maximum speed $v$ (in $\mathrm{m} {\mathrm{s}}^{-1}$) of the middle sphere after the system is released.

Three-point charges of $0.1 \mathrm{C}$ each are placed at the corners of an equilateral triangle with side $L=1 \mathrm{m}.$ If this system is supplied energy at the rate of $1 \mathrm{kW},$ how much time (in hour) will be required to move one of the charges to the midpoint of the line joining the other two?

A radioactive source in the form of a metal sphere of radius ${10}^{-2} \mathrm{m}$ emits beta particles (electrons) at the rate of $5\times {10}^{10}$ particles per second. The source is electrically insulated. How long will it take (in $\mathrm{\mu s}$) for its potential to be raised by $2 \mathrm{V}$ assuming that $40\%$ of the emitted beta particles escape from the source?

The figure shows four situations in which charges as indicated $\left(q>0\right)$ are fixed on an axis. How many situations is there a point to the left of the charges where an electron would be in equilibrium?

An electric field is given by $\overrightarrow{E}=\left(y\hat{\mathrm{i}}+x\hat{\mathrm{j}}\right) \mathrm{N} {\mathrm{C}}^{-1}$. Find the work done (in $\mathrm{J}$) in moving a $1 \mathrm{C}$ charge from ${\overrightarrow{r}}_{\mathrm{A}}=\left(2\hat{\mathrm{i}}+2\hat{\mathrm{j}}\right) \mathrm{m}$ to ${\overrightarrow{r}}_{\mathrm{B}}=\left(4\hat{\mathrm{i}}+\hat{\mathrm{j}}\right) \mathrm{m}$

The arrangement is shown consists of three elements.
a. A thin rod of charge $-3.0 \mu \mathrm{C}$ that forms a full circle of radius $6.0 \mathrm{cm}.$
b. A second thin rod of charge $2.0 \mu \mathrm{C}$ that forms a circular arc of radius $4.0 \mathrm{cm}$ and concentric with the full circle, subtending an angle of $90°$ at the centre of the full circle.
c. An electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude $1.28\times {10}^{-21} \mathrm{C} \mathrm{m}$
Find the net electric potential in volts at the centre.

An infinite plane of charge with $\sigma =2{\epsilon }_0 \mathrm{C} {\mathrm{m}}^{-2}$ is tilted at a $37°$ angle to the vertical direction as shown below. Find the potential difference, $V_A-V_B$ in volts, between points $A$ and $B$ at $5 \mathrm{m}$ distance apart (where $B$ is vertically above $A$).

A small sphere of mass $m=0.5 \mathrm{kg}$ carrying a positive charge $q=110 \mathrm{\mu C}$ is connected with a light, flexible and inextensible string of length $r=60 \mathrm{cm}$ and whirled in a vertical circle. If a vertically upward electric field of strength $E={10}^5 \mathrm{N} {\mathrm{C}}^{-1}$ exists in the space, calculate minimum velocity of sphere (in $\mathrm{m} {\mathrm{s}}^{-1}$) required at highest point so that it may just complete the circle. $\left(g=10{ \mathrm{m} \mathrm{s}}^{-2}\right)$