Electric Field

A charged ring having charge density as $\lambda ={\lambda }_0\cos \theta$. Find the electric B field at point$P(0,0, z)$.

When electric field is applied to the electrons in a conductor it starts

The graph showing the variation of electric field $\left(E\right)$ with the distance $\left(r\right)$ from the centre of a conducting spherical shell is - 

A ring of radius $R$with a uniformly distributed charge $q$ is shown in figure. A charge $q_0$is now placed at the centre of the ring. Find the increment in the tension in ring.

Two point charges $Q$ and $-3Q$ are placed at some distance apart. If the electric field at the location of $Q$ is $E$, the field at the location of $-3Q$ is

The force exerted by an electric field on a charge of $+10 \mathrm{\mu C}$ at a point is $16 \mathrm{x} {10}^{-4} \mathrm{N}.$ The intensity of electric field is
 

A charge of $4\times {10}^{-8} \mathrm{C}$ is distributed uniformly on the surface of a sphere of radius $1 \mathrm{cm}$. It is covered by a concentric, hollow conducting sphere of radius $5 \mathrm{cm}.$
(a) Find the electric field at a point $2 \mathrm{cm}$ away from the centre.
(b) A charge of $6\mathrm{x}{10}^{-8} \mathrm{C}$ is placed on the hollow sphere. Find the surface charge density on the outer surface of the hollow sphere.

A point charge $-50 \mathrm{\mu C}$ is located at $(2, 3)$. Find electric field at $(8, -5)$.

The charge $Q=\pi \mathrm{C}$ is distributed on thin semicircular ring of radius $R=2 \mathrm{m}$. There is a uniform electrostatic field $\left|\overrightarrow{E}\right|=2 \mathrm{N} {\mathrm{C}}^{-1}$ directed horizontally. The semicircular ring can rotate freely about a fixed vertical axis $AB$. Initially the ring is in static equilibrium as shown in figure. If we want to rotate it about the fixed axis by $90°$, then minimum work required on the ring is $x \mathrm{J}$. Find the value of $x$.

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Two charges $\sqrt{3}\mathrm{C}$ and $q \mathrm{C}$ are placed at $\left(2,0\right)$ and $\left(0,2\right)$. The direction of intensity of electric field at $\left(2,2\right)$ makes an angle $30°$ with $y‐$axis then $q$ is :

Two unlike charges $Q_1$ and $Q_2$ are positioned at point $\left(0,0\right)$ and $\left(2 \mathrm{mm},0\right)$ as shown in the figure. The graph between the field strength at any point on the $x$-axis, to the right of the charge $Q_2$ varies according to a law that is represented schematically in the figure (2). The field strength is assumed to be positive if its direction coincides with the positive direction on the $x$-axis. The field strength is zero at point $B\left[\frac{4\sqrt{2}}{2\sqrt{2}-1} \mathrm{mm},0\right]$ and is maximum at point $C$. The charges $Q_1$ and $Q_2$ are respectively

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A block of mass $m$ and charge $q$ is connected to a point $O$ with help of an inextensible string. The system is on a horizontal table. An electric field is switched on in direction perpendicular to string. What will be tension in string when it become parallel to electric field?

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A charge particle is released from rest in an uniform electric field for $2 \mathrm{s}$ its $\mathrm{KE}$ is $20 \mathrm{J}$. If the same charge particle from state of rest is allowed to accelerate for $3 \mathrm{s}$, its $\mathrm{KE}$ will be

A thin rigid insulating ring of radius $r$ and mass $m$ has a very small gap of length $l\left(l<r\right)$ and carries a uniformly distributed charge $q$. The ring is at rest in free space and a uniform electric field $E$ in the plane of the ring and parallel to the gap is switched on as shown in the figure. Find the maximum angular speed of the ring in subsequent motion.

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The electric field at $\left(30,30\right) \mathrm{cm}$ due to a charge $-8 \mathrm{nC}$ at the origin in $\mathrm{N} {\mathrm{C}}^{-1}$ is

A particle of charge $-q$ revolves around a long cylinder radius of radius $R$ charge density $\rho$. Find the kinetic energy of the charge

A proton and an $\alpha$ particle having equal kinetic energy are projected in a uniform transverse electric field as shown in figure

A circular metal plate of radius $1.5 \mathrm{cm}$ is charged with $10 \mathrm{\mu C}$ situated in air. If the same circular plate carrying same charge were kept in acetone, what would be magnitude of mechanical force? ($k_{\mathrm{acetone}}$ $=27$)

An arc of radius $r$, lying in the first quadrant is shown in the figure. The linear charge density on the arc is $\lambda$. The magnitude and direction of electric field intensity at the point of origin is