The linear charge densities of two infinitely | vedclass

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

Question

(B) The electric field $E$ due to an infinitely long wire with linear charge density $\lambda$ at a distance $r$ is given by $E = \frac{\lambda}{2 \pi

Vedclass · Accepted Answer

$36 	imes 10^{11} \ NC^{-1}$

Vedclass · Answer

(B) The electric field $E$ due to an infinitely long wire with linear charge density $\lambda$ at a distance $r$ is given by $E = \frac{\lambda}{2 \pi \epsilon_0 r} = \frac{2k\lambda}{r}$,where $k = 9 	imes 10^9 \ Nm^2C^{-2}$.Given $\lambda_1 = 4 \ Cm^{-1}$,$\lambda_2 = 8 \ Cm^{-1}$,and separation $d = 4 \ cm = 0.04 \ m$.The midpoint is at distance $r = d/2 = 0.02 \ m$ from both wires.The electric field due to wire $1$ is $E_1 = \frac{2 	imes 9 	imes 10^9 	imes 4}{0.02} = 36 	imes 10^{11} \ NC^{-1}$ (directed away from wire $1$).The electric field due to wire $2$ is $E_2 = \frac{2 	imes 9 	imes 10^9 	imes 8}{0.02} = 72 	imes 10^{11} \ NC^{-1}$ (directed away from wire $2$).Since both wires have positive charge densities,the fields at the midpoint are in opposite directions.The net electric field is $E_{net} = |E_2 - E_1| = |72 	imes 10^{11} - 36 	imes 10^{11}| = 36 	imes 10^{11} \ NC^{-1}$.

The linear charge densities of two infinitely long thin and parallel wires are $4 \ Cm^{-1}$ and $8 \ Cm^{-1}$,and the separation between them is $4 \ cm$. The electric field intensity at the midpoint on the line joining them is:

Similar Questions

$A$ cube of a metal is given a positive charge $Q$. For the above system,which of the following statements is true?

$A$ charge of $1 \mu C$ each is placed on five corners of a regular hexagon of side $1 \ m$. The electric field at its centre is . . . . . . $N$/$C$.

The distance between a proton and an electron in a hydrogen atom is ${10^{ - 10}} \ m$. Both have a charge of magnitude $1.6 \times {10^{ - 19}} \ C$. The magnitude of the electric field intensity produced at the position of the electron due to the proton is:

Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is $30^{\circ} .$ The electric field in the region shown between them is given by

If the potential at the centre of a uniformly charged hollow sphere of radius $R$ is $V$,then the electric field at a distance $r$ from the centre of the sphere is $(r > R)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module