Electric Field and Potential

A particle of charge+q and mass m moving under the influence of a uniform electric field E $\widehat{\text{i}}\text{and magnetic field B}\widehat{\text{k}}$enters in I quadrant of a coordinate system at a point (0, a) with initial velocity v$\widehat{\text{i}}$and leaves the quadrant at a point (2a, 0) with velocity $-\mathrm{2 }\text{v}\widehat{\text{j}}$.
Find Rate of work done by the electric field at point (0, a)

A charge $+Q$ is placed on a large spherical conducting shell of radius $R$. Another small conducting sphere of radius r carrying charge $q$ is introduced inside the large shell and is placed at its centre. The potential difference between two points, one lying on the sphere and the other on the shell would be:

How does the electric potential due to a dipole vary on the dipole axis as a function of $r$– distance of the field point from the mid–point of the dipole, at large distances?

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge $Q$. A charge $q$ is placed at the centre of the shell.
What is the surface charge density on the (i) inner surface, (ii) outer surface of the shell?

Figure shows two uniform charged concentric spherical shells. Both charges are positive. Select correct statement(s):

Six charges are placed around a regular hexagon of side length $a$ as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center $O$ of the hexagon and is bisected by the side.

Which of the following statement(s) is(are) correct in SI units?

State differences between electric potential and electric flux.

A region in space contains a total positive charge $Q$ that is distributed spherically such that the volume charge density is given by

$\rho \left(r\right)=\left\{\begin{array}{rll}\alpha & \mathrm{for}& r\le \frac{R}{2}\\ 2\alpha \left[1-\frac{r}{R}\right]& \mathrm{for}& \frac{R}{2}\le r\le R\\ 0& \mathrm{for}& r\ge R\end{array}\right.$

Where $\alpha$ a positive constant and $r$ is distance from origin. Then

A uniform electric field of $500 \mathrm{V} {\mathrm{m}}^{–1}$ is directed at $150°$ to the positive $X$-axis, in the $X-Y$ plane as shown in figure:-

Consider a solid neutral conducting sphere of radius $2R$ having a concentric cavity of radius $R.$ Points $A, D, B$ are at distances $3R, \frac{3R}{2}$ and $\frac{R}{2}$ from centre $C$ respectively. $s_1$ and $s_2$ are inner surface and outer surface of the hollow sphere. $\left(k=\frac{1}{4\pi {\epsilon }_0}\right)$ Mark the CORRECT statement:

Which of the following options are CORRECT about a non conducting, thin circular disk of radius $R$ and uniform surface charge density $\sigma .$

(Assume electrostatic potential at infinity to be zero)

The resistivity of a cylindrical conductor carrying steady current along its length varies linearly with the distance from the current carrying end as given by $\rho ={\rho }_0\left(1+\frac{x}{l}\right)$ where $l$ is the length of the conductor and $x$ is the distance from the current entry end. ${\rho }_o$ is a positive constant.

Three uniformly charged infinite wires with linear charge density $\lambda$ are placed along $x, y$ and $z$ axis respectively. Find the flux of electric field through Gaussian surface given by $x^2+y^2+z^2=1:x>0;y>0;z>0$ If your answer is $\frac{n\lambda }{12{ϵ}_0}$  fill the value of $n$

A charge $2\times {10}^{-3} \mathrm{C}$ and the mass $1 \mathrm{gm}$ is projected from level ground with a velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle of with the $37°$, horizontal ($x$ direction). The electric potential in space is given by, $V=3x+4y$. What is the speed of the charge (in $\mathrm{m} {\mathrm{s}}^{-1}$ ) when its $y$, coordinate is maximum?

Three charged conducting concentric spherical shells have radii $r, 2r$ and $3r$ respectively. They carry charges $q_1,q_2$ and $q_3$ respectively, after innermost and outermost shells are earthed. Then find $\frac{q_3}{q_1}$

A region is space contains a total positive charge $Q$ that is distributed spherically such that the volume charge density is given by

$\rho \left(r\right)=\left\{\begin{array}{llc}\alpha & \mathrm{for} & r\le \frac{R}{2}\\ 2\alpha \left[1-\frac{r}{R}\right]& \mathrm{for} & \frac{R}{2}\le r\le R\\ 0& \mathrm{for} & r\ge R\end{array}\right.$

Where $\alpha$ is a positive constant. Then

Figure shows three spherical shells in separate situations, with each shell having the same uniform positive net charge. Points $1, 4$ and $7$ are at the same radial distances from the centre of the their respective shells; so are points $2,5$ and $8$; and so are points $3,6$ and $9$. With the electric potential taken equals to zero at an infinite distance, choose correct statement.

An insulated sphere with dielectric constant $K$ (where $K>1$) of radius of $R$ is having a total charge $+Q_0$ uniformly distributed in the volume. It is kept inside a metallic sphere of inner radius $2\mathrm{R}$ and outer radius $3\mathrm{R}$. Whole system is kept inside a metallic shell of radius $4\mathrm{R}$, metallic sphere is earthed as shown in the figure. Spherical shell of radius $4\mathrm{R}$ is given a charge $+Q_0$. Consider $E-r$ graph for $r>0$ only. Where $E$ and $r$ represents electric field and radial distance from the centre respectively. Then choose the CORRECT option(s)