Electric Field

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

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?

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?

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

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.

Three particles of charges $1\times {10}^{-8} \mathrm{C}, 8.0\times {10}^{-8} \mathrm{C}$ and $27\times {10}^{-8} \mathrm{C}$ are kept fixed on the $x$-axis at point $x=10 \mathrm{cm}, 20 \mathrm{cm}$ and $30 \mathrm{cm}$ respectively. The magnitude of the electric force acting on a $1 \mathrm{C}$ charge placed at $x=0.$ (Assume $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9 \mathrm{N} {\mathrm{C}}^{-2} {\mathrm{m}}^2$)

A solid metal sphere with a spherical cavity as shown below has a total charge $Q.$ Let $O$ be the centre of the sphere and $P$ and $Q$ are two points equidistant from it $\left(\left|\overrightarrow{OP}\right|=\left|\overrightarrow{OQ}\right|\right)$. If $\left|{\overrightarrow{E}}_p\right|$ and $\left|{\overrightarrow{E}}_Q\right|$ are magnitude of electric field at $P$ and $Q$ respectively, then the correct statement is

Two fixed point charges $+4q$ and $+q$ units are separated by a distance of $a$. The distance, where the resultant electric field intensity is zero, measured from charge $+4q$ is

The surface charge density of a thin charged disc of radius $R$ is $\sigma .$ The value of the electric field at the centre of the disc is $\frac{\sigma }{2{\in }_0}$.

With respect to the field at the centre, the electric field along the axis at a distance $R$ from the centre of the disc :

Two large parallel plates carry the charge of equal magnitude, one positive and the other negative, that is distributed uniformly over their inner surfaces. Rank the points $1$ through $5$ according to the magnitude of the electric field at the points, least to greatest.