A long cylindrical volume contains a uniformly distributed charge of density ρ Cm ^{-3} . electric

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1. Electric Charges and Fields

hard

A long cylindrical volume contains a uniformly distributed charge of density $\rho \;Cm ^{-3}$. The electric field inside the cylindrical volume at a distance $x =\frac{2 \varepsilon_{0}}{\rho} m$ from its axis is $.......Vm ^{-1}$

A

$2$

B

$1$

C

$0$

D

$3$

(JEE MAIN-2022)

Solution

$\int Eds \cos 0=\frac{ q }{\varepsilon_{0}}$

$\Rightarrow E \cdot 2 \pi \times xh =\frac{\rho \times \pi x ^{2} h }{\varepsilon_{0}}$

$\Rightarrow E =\frac{\rho x }{2 \varepsilon_{0}}$

$\Rightarrow E =\frac{\rho}{2 \varepsilon_{0}} \times \frac{2 \varepsilon_{0}}{\rho}=1$

Standard 12

Physics

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