An infinite line charge produces a field of 7 | 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 infinite line charge is given by the formula: $E = \frac{\lambda}{2\pi\varepsilon_0 r}$.Given values are: $E = 7.

Vedclass · Accepted Answer

$7.98 	imes 10^{-4} \, C/m$

Vedclass · Answer

(B) The electric field $E$ due to an infinite line charge is given by the formula: $E = \frac{\lambda}{2\pi\varepsilon_0 r}$.Given values are: $E = 7.182 	imes 10^8 \, N/C$ and $r = 2 \, cm = 2 	imes 10^{-2} \, m$.We know that $\frac{1}{4\pi\varepsilon_0} = 9 	imes 10^9 \, N \cdot m^2/C^2$,so $\frac{1}{2\pi\varepsilon_0} = 2 	imes 9 	imes 10^9 = 18 	imes 10^9$.Rearranging the formula for linear charge density $\lambda$: $\lambda = E \cdot r \cdot (2\pi\varepsilon_0) = \frac{E \cdot r}{2 \cdot (1 / 4\pi\varepsilon_0)}$.Substituting the values: $\lambda = \frac{7.182 	imes 10^8 	imes 2 	imes 10^{-2}}{2 	imes 9 	imes 10^9}$.$\lambda = \frac{7.182 	imes 10^6}{18 	imes 10^9} = 0.399 	imes 10^{-3} \, C/m = 3.99 	imes 10^{-4} \, C/m$.Wait,recalculating: $\lambda = \frac{7.182 	imes 10^8 	imes 2 	imes 10^{-2}}{18 	imes 10^9} = \frac{14.364 	imes 10^6}{18 	imes 10^9} = 0.798 	imes 10^{-3} = 7.98 	imes 10^{-4} \, C/m$.

List-$I$	List-$II$
$(A)$ Electric field inside (distance $r < R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$.	$(I)$ $\sigma / \varepsilon_0$
$(B)$ Electric field at distance $r$ from a uniformly charged infinite plane sheet with surface charge density $\sigma$.	$(II)$ $\sigma / 2 \varepsilon_0$
$(C)$ Electric field outside (distance $r > R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$.	$(III)$ $0$
$(D)$ Electric field between $2$ oppositely charged infinite plane parallel sheets with uniform surface charge density $\sigma$.	$(IV)$ $\frac{\sigma R^2}{\varepsilon_0 r^2}$

An infinite line charge produces a field of $7.182 \times 10^8 \, N/C$ at a distance of $2 \, cm$. The linear charge density is

Similar Questions

$A$ hollow cylinder has a charge $q$ within it. If $\phi$ is the electric flux in units of $V-m$ associated with the curved surface $B,$ the flux linked with the plane surface $A$ in units of $V-m$ will be

$A$ and $B$ are two concentric spheres. If $A$ is given a charge $Q$ while $B$ is earthed as shown.

$\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$. The electric field at any point on the surface of the spherical shell is:

An infinite line charge produces a field of $9 \times 10^4 \ NC^{-1}$ at a distance of $2 \ cm$. Its linear charge density is

Vedclass Test Series

Exam Paper Generator

Online Exam Module