Two parallel infinite line charges with linea | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The electric field due to an infinite line charge at a distance $r$ is given by $E = \frac{\lambda}{2\pi\epsilon_0 r}$.Let the two line charges be

Vedclass · Accepted Answer

$\frac{\lambda}{\pi\epsilon_0 R}\; N/C$

Vedclass · Answer

(C) The electric field due to an infinite line charge at a distance $r$ is given by $E = \frac{\lambda}{2\pi\epsilon_0 r}$.Let the two line charges be $1$ and $2$,separated by a distance $2R$. The mid-point $P$ is at a distance $R$ from both lines.The electric field $\overrightarrow{E}_1$ due to the positive line charge at $P$ points away from it (towards the negative line charge),so $E_1 = \frac{\lambda}{2\pi\epsilon_0 R}$.The electric field $\overrightarrow{E}_2$ due to the negative line charge at $P$ points towards it (in the same direction as $\overrightarrow{E}_1$),so $E_2 = \frac{|-\lambda|}{2\pi\epsilon_0 R} = \frac{\lambda}{2\pi\epsilon_0 R}$.Since both fields are in the same direction,the net electric field is $E = E_1 + E_2 = \frac{\lambda}{2\pi\epsilon_0 R} + \frac{\lambda}{2\pi\epsilon_0 R} = \frac{2\lambda}{2\pi\epsilon_0 R} = \frac{\lambda}{\pi\epsilon_0 R}\; N/C$.

Two parallel infinite line charges with linear charge densities $+\lambda\; C/m$ and $-\lambda\; C/m$ are placed at a distance of $2R$ in free space. What is the electric field mid-way between the two line charges?

Similar Questions

The electrostatic field of a long uniformly charged wire varies with distance $r$ according to which relation?

$A$ solid ball of radius $R$ has a charge density $\rho$ given by $\rho = \rho_0 \left( 1 - \frac{r}{R} \right)$ for $0 \leq r \leq R$. The electric field outside the ball is

An electric field converges at the origin whose magnitude is given by the expression $E = 100\,r\,N/C$,where $r$ is the distance measured from the origin.

The electric field at a distance of $20 \ cm$ from the center of a charged spherical shell of radius $10 \ cm$ is $100 \ V/m$. What is the electric field at a distance of $3 \ cm$ from the center?

The figure shows the graph of electric field $E(r)$ versus distance $(r)$ from the center of an object. Therefore,...

Vedclass Test Series

Exam Paper Generator

Online Exam Module