Electrostatics

JEE Main level, single correct, medium

223 of 311

Question 223 of 311

This question has statement 11 and statement 22 . Of the four choices given after the statements, choose the one that best describes the two statements.
An insulating solid sphere of radius
R\mathrm{R} has a uniformly positive charge density ρ\rho. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero.
Statement
11: When a charge qq is taken from the centre to the surface of the sphere, its potential energy changes by qp3ε0\frac{\mathrm{qp}}{3 \varepsilon_0}
Statement
22: The electric field at a distance r(r<R)r(r \lt R) from the centre of the sphere is ρr3ε0\frac{\rho r}{3 \varepsilon_0}

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Answer: (C) Statement 11 is false, Statement 22 is true

∮E→⋅d→A=1ε0(ρ×43πr3)\oint \overrightarrow{\mathrm{E}} \cdot \overrightarrow{\mathrm{d}} \mathrm{A}=\frac{1}{\varepsilon_0}\left(\rho \times \frac{4}{3} \pi \mathrm{r}^3\right)
E=ρr3ε0\mathrm{E}=\frac{\rho \mathrm{r}}{3 \varepsilon_0}
Statement
22 is correct
ΔPE=(Vsur −Vcent )q=−q6ε0ρR2\Delta \mathrm{PE}=\left(\mathrm{V}_{\text {sur }}-\mathrm{V}_{\text {cent }}\right) \mathrm{q}=-\frac{\mathrm{q}}{6 \varepsilon_0} \rho \mathrm{R}^2
Statement
11 is incorrect

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