A spherical volume contains a uniformly distr | vedclass

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

Question

(D) Given,the volume charge density of the sphere is $ho_v = 1 	imes 10^{-6} \ C/m^3$.The constant $\frac{1}{4 \pi \epsilon_0} = 9 	imes 10^9 \ Nm

Vedclass · Accepted Answer

$12 \pi$

Vedclass · Answer

(D) Given,the volume charge density of the sphere is $ho_v = 1 	imes 10^{-6} \ C/m^3$.The constant $\frac{1}{4 \pi \epsilon_0} = 9 	imes 10^9 \ Nm^2 C^{-2}$.The distance from the centre is $r = 1 \ mm = 10^{-3} \ m$.For a point inside a uniformly charged sphere,the electric field $E$ is given by Gauss's Law as:$E = \frac{ho_v r}{3 \epsilon_0}$Since $\frac{1}{4 \pi \epsilon_0} = 9 	imes 10^9$,we have $\frac{1}{\epsilon_0} = 36 \pi 	imes 10^9$.Substituting this into the formula:$E = \frac{ho_v r}{3} 	imes (36 \pi 	imes 10^9)$$E = ho_v r 	imes 12 \pi 	imes 10^9$Substituting the values of $ho_v$ and $r$:$E = (1 	imes 10^{-6}) 	imes (10^{-3}) 	imes 12 \pi 	imes 10^9$$E = 10^{-9} 	imes 12 \pi 	imes 10^9$$E = 12 \pi \ N/C$.Therefore,the electric field is $12 \pi \ N/C$.

$A$ spherical volume contains a uniformly distributed charge of density $1.0 \times 10^{-6} \ C/m^3$. Find the electric field (in $N/C$) at a point inside the volume at a distance $1 \ mm$ from the centre. (Let $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \ Nm^2 C^{-2}$)

Similar Questions

An infinite nonconducting sheet of charge has a surface charge density of $10^{-7} \ C/m^2$. The separation between two equipotential surfaces near the sheet whose potential differ by $5 \ V$ is:

Two infinitely long thin straight parallel wires are kept at a perpendicular distance of $2R$, having uniform linear charge densities $+\lambda$ and $-\lambda$ respectively. The magnitude of the electric field at the midpoint between the two wires will be . . . . . . .

Consider the force $F$ on a charge $q$ due to a uniformly charged spherical shell of radius $R$ carrying charge $Q$ distributed uniformly over it. Which one of the following statements is true for $F$,if $q$ is placed at distance $r$ from the centre of the shell?

If $q$ is the charge per unit area on the surface of a conductor,then the electric field intensity at a point on the surface is

Vedclass Test Series

Exam Paper Generator

Online Exam Module