B M Sharma Solutions for Chapter: Electric Potential, Exercise 1: Concept Application Exercise

Find out the following :

a) $V_{\mathrm{A}} - V_{\mathrm{B}}$

b) $V_{\mathrm{B}}-V_{\mathrm{C}}$

c) $V_{\mathrm{C}}-V_{\mathrm{A}}$

d) $V_{\mathrm{D}}-V_{\mathrm{C}}$

e) $V_{\mathrm{A}}-V_{\mathrm{D}}$

f) Arrange the order of potential for points $A, B, C \text{and} D$.

Find potential difference $\left(V_{\mathrm{ab}}\right)$ between points $a \text{and} b$ in an electric field $\overrightarrow{E}=\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}}\right) \mathrm{N} {\mathrm{C}}^{-1}$, where $\overrightarrow{r_{\mathrm{a}}}=\left(\hat{\mathrm{i}}-2\hat{\mathrm{j}}+\hat{\mathrm{k}}\right) \mathrm{m}$ and $\overrightarrow{r_{\mathrm{b}}}=\left(2\hat{\mathrm{i}}+\hat{\mathrm{j}}-2\hat{\mathrm{k}}\right) \mathrm{m}$.

At a point due to a point charge, the values of electric field intensity and potential are $32 \mathrm{N} {\mathrm{C}}^{-1}$ and $16 \mathrm{J} {\mathrm{C}}^{-1}$ respectively. Calculate the magnitude of the charge and calculate the distance of the charge from the point of observation.

Two uniformly charged large plane sheets $S_1$ and $S_2$ having charge densities ${\sigma }_1$ and ${\sigma }_2\left({\sigma }_1>{\sigma }_2\right)$ are placed at a distance $d$ parallel to each other. A charge $q_0$ is moved along a line of length $a \left(a<d\right)$ at an angle ${45}^{°}$ with the normal to $S_1$. Calculate the work done by the electric field.

The figure shows field lines and equipotential (dashed) lines. 

(a) Find the external work done to move a $-2 \mathrm{\mu C}$  charge at constant speed from $A$ to $B$ along the path shown. 

(b) Find the work done by the electric field.

In moving from $A$ to $B$ along an electric field, the electric field does $4.8\times {10}^{-19} \mathrm{J}$ of work on an electron in the field illustrated in the figure. What are the differences in the electric potential? Find the potential difference a) $V_{\mathrm{B}}-V_{\mathrm{A}}$ b)  $V_{\mathrm{C}}-V_{\mathrm{A}}$ c) ${\mathrm{V}}_{\mathrm{C}}-{\mathrm{V}}_{\mathrm{B}}$

A charge $q_0$ is transported from point $A$ to $B$ along the arc $AB$ with centre at $C$ as shown in the figure near a long charged wire with linear density $\mathrm{\lambda }$ lying in the same plane. Find the work done by the external agent in doing so.

The graphical variation of electric potential due to point charge $q_1$ and $q_2$ lies on the $x$-axis at some separation $d$, which is shown in the figure. If the origin is the point between the charges where potential is zero. Distance of $q_2$ from origin is $\frac{d}{4}$. Find the distance of point $P$ (marked in the figure) from charge $q_2$.