An infinite line of charge with uniform line | vedclass

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

Question

(B) The electric field due to an infinite line charge at a distance $r$ is given by $E_{line} = \frac{2k\lambda}{r}$.The electric field due to a point

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) The electric field due to an infinite line charge at a distance $r$ is given by $E_{line} = \frac{2k\lambda}{r}$.The electric field due to a point charge $q$ at a distance $(d-r)$ from it is $E_{point} = \frac{kq}{(d-r)^2}$.For the total electric field to be zero,the magnitudes must be equal: $E_{line} = E_{point}$.Substituting the values $\lambda = 1 \ C \ m^{-1}$,$q = 1 \ C$,and $d = 3 \ m$:$\frac{2k(1)}{r} = \frac{k(1)}{(3-r)^2}$$\frac{2}{r} = \frac{1}{(3-r)^2}$$2(3-r)^2 = r$$2(9 - 6r + r^2) = r$$18 - 12r + 2r^2 = r$$2r^2 - 13r + 18 = 0$Using the quadratic formula $r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:$r = \frac{13 \pm \sqrt{169 - 144}}{4} = \frac{13 \pm 5}{4}$$r_1 = \frac{18}{4} = 4.5 \ m$ and $r_2 = \frac{8}{4} = 2 \ m$.Since the point must be between the origin and the charge $(0 < r < 3)$,the valid distance is $r = 2 \ m$.

Similar Questions

The electric field at $20 \,cm$ from the centre of a uniformly charged non-conducting sphere of radius $10 \,cm$ is $E$. Then at a distance $5 \,cm$ from the centre it will be

Consider a uniform spherical volume charge distribution of radius $R$. Which of the following graphs correctly represents the magnitude of the electric field $E$ at a distance $r$ from the centre of the sphere?

$A$ hollow metal sphere of radius $R$ is uniformly charged. The electric field due to the sphere at a distance $r$ from the centre is:

$A$ thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E(r)$ produced by the shell in the range $0 \le r < \infty$,where $r$ is the distance from the centre of the shell?

Vedclass Test Series

Exam Paper Generator

Online Exam Module