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JEE Main 2022 (27 Jul, Shift 1) · Electric Flux & Gauss's Law

Electric Flux & Gauss's Law question from JEE Main 2022 (27 Jul, Shift 1)

Q74JEE Main 2022 · 27 JUL · SHIFT 1Easy

Electric Flux & Gauss's Law

A long cylindrical volume contains a uniformly distributed charge of density ρ C m−3\rho\text{ C m}^{-3}. The electric field inside the cylindrical volume at a distance x=2ε0ρ mx = \frac{2\varepsilon_0}{\rho}\text{ m} from its axis is ________ V m−1\text{V m}^{-1}.

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Answer: 1

  1. Gaussian cylinder of radius xx, length LL: E⋅2πxL=ρπx2Lε0E \cdot 2\pi x L = \dfrac{\rho \pi x^2 L}{\varepsilon_0}
  2. E=ρx2ε0E = \dfrac{\rho x}{2\varepsilon_0}
  3. Put x=2ε0ρx = \dfrac{2\varepsilon_0}{\rho}: E=ρ2ε0⋅2ε0ρ=1E = \dfrac{\rho}{2\varepsilon_0}\cdot\dfrac{2\varepsilon_0}{\rho} = 1
  4. So E=1E = 1 V m−1^{-1}.
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