Obtain expression of electric field by a straight wire of infinite length and with linear charge den

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1. Electric Charges and Fields

hard

Obtain the expression of electric field by a straight wire of infinite length and with linear charge density $'\lambda '$.

Option A

Option B

Option C

Option D

Solution

Consider an infinitely long thin straight wire with uniform linear charge density $\lambda$.

Suppose we take the radial vector from $\mathrm{O}$ to $\mathrm{P}$ and rotate it around the wire. The points $\mathrm{P}, \mathrm{P}^{\prime}$,

$\mathrm{P}^{\prime \prime}$ so obtained are completely equivalent with respect to the charged wire.

This implies that the electric field must have the same magnitude at these points.

The direction of electric field at every point must be radial (outward if $\lambda>0$, inward $\lambda<0$ ).

Since the wire is infinite, electric field does not depend on the position of $\mathrm{P}$ along the length of

the wire.

The electric field is everywhere radial in the plane cutting the wire normally and its magnitude

depends only on the radial distance $r .$

Imagine a cylindrical Gaussian surface as shown in figure.

Since the field is everywhere radial, flux through the two ends of the cylindrical Gaussian surface

is zero.

At the cylindrical part of the surface $\overrightarrow{\mathrm{E}}$ is normal to the surface at every point and its magnitude

is constant since it depends only on $r .$

The surface area of the curved part is $2 \pi r l$, where $l$ is the length of the cylinder.

Flux through the Gaussian surface,

$=$ flux through the curved cylindrical part of the surface

$=E \times 2 \pi r l$

Standard 12

Physics

Two concentric conducting thin spherical shells of radii $a$ and $b\ (b > a)$ are given charges $Q$ and $ -2Q$ respectively. The electric field along a line passing through centre as a function of distance $(r)$ from centre is given by

medium

Two fixed, identical conducting plates $(\alpha $ and $\beta )$, each of surface area $S$ are charged to $-\mathrm{Q}$ and $\mathrm{q}$, respectively, where $Q{\rm{ }}\, > \,{\rm{ }}q{\rm{ }}\, > \,{\rm{ }}0.$ A third identical plate $(\gamma )$, free to move is located on the other side of the plate with charge $q$ at a distance $d$ as per figure. The third plate is released and collides with the plate $\beta $. Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst $\beta $ and $\gamma $.

$(a)$ Find the electric field acting on the plate $\gamma $ before collision.

$(b)$ Find the charges on $\beta $ and $\gamma $ after the collision.

$(c)$ Find the velocity of the plate $\gamma $ after the collision and at a distance $d$ from the plate $\beta $.

hard

If a small sphere of mass $m$ and charge $q$ is hung from a silk thread at an angle $\theta$ with the surface of a vertical charged conducting plate, then for equilibrium of sphere, the surface charge density of the plate is

medium

An isolated sphere of radius $R$ contains uniform volume distribution of positive charge. Which of the curve shown below, correctly illustrates the dependence of the magnitude of the electric field of the sphere as a function of the distance $r$ from its centre?

normal

(KVPY-2011)

Consider a sphere of radius $R$ with charge density distributed as :

$\rho(r) =k r$, $r \leq R $

$=0$ for $r> R$.

$(a)$ Find the electric field at all points $r$.

$(b)$ Suppose the total charge on the sphere is $2e$ where e is the electron charge. Where can two protons be embedded such that the force on each of them is zero. Assume that the introduction of the proton does not alter the negative charge distribution.

medium

Obtain the expression of electric field by a straight wire of infinite length and with linear charge density $'\lambda '$.

Solution

Similar Questions

Two concentric conducting thin spherical shells of radii $a$ and $b\ (b > a)$ are given charges $Q$ and $ -2Q$ respectively. The electric field along a line passing through centre as a function of distance $(r)$ from centre is given by

If a small sphere of mass $m$ and charge $q$ is hung from a silk thread at an angle $\theta$ with the surface of a vertical charged conducting plate, then for equilibrium of sphere, the surface charge density of the plate is

An isolated sphere of radius $R$ contains uniform volume distribution of positive charge. Which of the curve shown below, correctly illustrates the dependence of the magnitude of the electric field of the sphere as a function of the distance $r$ from its centre?

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