Electric Field

Consider a set of $12$ equal charges ($+\mathrm{q}$ each), arranged to form two concentric regular hexagons in the $\mathrm{xy}$-plane, centred at origin. The edges of the two hexagons have lengths $\mathrm{a}$ and $2\mathrm{a}$ respectively. They are arranged in such a way that two vertices of each one of them are on the $\mathrm{y}$-axis. Suppose that the charges from the vertices at $(0,2\mathrm{a})$ and $(0,-\mathrm{a})$ are removed. Then, the magnitude of the electric field produced by the resulting configuration at the origin is

Consider two semi-infinite flat plates lying parallel to the $x,y$-plane at $z=+d$ and $z=-d$, carrying uniform surface charge densities $+\sigma$ and $-\sigma$, respectively. The plates extend from $x=0$ to $x=-\infty$ and from $y=-\infty$ to $y=+\infty$. The direction of the electric field at a point whose coordinates are $\left(0,0,2d\right)$ is along

In a conducting metallic sphere of radius $2r$, an spherical cavity of radius $r$ is made. A charge $q$ is kept at the centre of the cavity as shown in the figure. Find the magnitude of the total electric field at $\left(4r, 0, 0\right).$

Assertion: Due to two point charges electric field and electric potential cannot be zero at some point simultaneously.

Reason: Field is a vector quantity and potential is a scalar quantity.

Two point charges $q$ and $2q$ are placed some distance apart. If the electric field at the location of $q$ be $E$, then that at the location of $2q$ will be

Two equal positive charges $\left(q\right)$ are placed at the vertices $B$ and $C$ of an isosceles triangle of base $a$ and height $h=3\sqrt{3}\frac{a}{2}$, as shown in the adjacent figure. When a charge $q^{\text{'}}$ is placed at $A,$ it is found that at a point inside the triangle, the net electric field due to the three charges vanishes. If this point is at a height $\frac{h}{3},$ then what is $q^{\text{'}}$?

The tracks of three charged particles in a uniform electrostatic field are shown in the figure. Which particle has the highest charge to mass ratio?

If the flux of the electric field through a closed surface is zero then

The constant $\mathrm{k}$ in Coulomb’s law depends on

A metallic shpere is placed in a uniform electric field. The line of force follow the path(s) shown in the figure as,

The maximum field intensity on the axis of a uniformly charged ring of charge $q$ and radius $R$ will be

A thin conducting ring of radius $R$ is given a charge $+Q$. The electric field at the centre $O$ of the ring due to the charge on the part $AKB$ of the ring is $E$. The electric field at the centre due to the charge on the part $ACDB$ of the ring is

The tracks of three charged particles in a uniform electrostatic field are shown in the figure. Which particle has the highest charge to mass ratio?

Two point charges of $20 \mu \mathrm{C}$ and $80 \mu \mathrm{C}$ are $10 \mathrm{cm}$ apart where will the electric field strength be zero on the line joining the charges from $20 \mu \mathrm{C}$ charge

A small metal ball is suspended in an uniform electric field with the help of an insulated thread. If a high energy $\mathrm{X}$-ray beam falls on the ball, then the ball

The electric intensity outside a charged sphere of radius $R$ at a distance $r(r>R)$ is

The minimum strength of a uniform electric field that can tear a conducting neutral thin-walled sphere into two equal parts is known to be $E_0$. Then determine the minimum electric field strength required to tear a sphere of one-fourth of the radius with the same wall thickness.

Two mutually perpendicular infinitely long straight conductors carrying uniformly distributed charges of linear densities ${\lambda }_1$ and ${\lambda }_2$ are positioned at a distance $r$ from each other.

Force between the conductors depends on $r$ as

An electrostatic field line leaves at an angle $\alpha$ from point charge $q_1$ and connects with point charge $-q_2$ at an angle $\beta$($q_1$and $q_2$ are positive) see figure below. If $q_2=\frac{3}{2}{q}_1$ and $\alpha =30°,$ then