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AIIMS 201826 May
Exam
AIIMS
Year
2018
Date
26 May
Subject
Physics
Chapter
Electrostatics

AIIMS 2018 · 26 May · Physics · Electrostatics

A long solid non-conducting cylinder of radius R is charged such...

A long solid non-conducting cylinder of radius RR is charged such that the volume charge density is proportional to rr where rr is the distance from axis. The electric field EE at a distance r(r<R)r(r < R) will depend on rr asA long solid non-conducting cylinder of radius R is charged such that the volume charge density is proportional to r

Options

  1. AE∝rE \propto r
  2. BE∝r2E \propto r^2
  3. CE∝(1/r)E \propto(1 / r)
  4. DE∝(1/r2)E \propto\left(1 / r^2\right)

Correct answer

B. E∝r2E \propto r^2

Step-by-step solution

(b):ρ∝r;ρ=KrdQ=ρV=Kr(2πrdr)×l\begin{aligned} & (\mathbf{b}): \rho \propto r ; \rho=K r \\ & d Q=\rho V \\ & \quad=K r(2 \pi r d r) \times l\end{aligned} Using Gauss's Law, E.2πrl=∫0rKr.2πrl.drε0⇒E=Kr23ε0∴E∝r2\begin{aligned} & E .2 \pi r l=\frac{\int_0^r K r .2 \pi r l . d r}{\varepsilon_0} \\ & \Rightarrow E=K \frac{r^2}{3 \varepsilon_0} \\ & \therefore E \propto r^2\end{aligned} A long solid non-conducting cylinder of radius R is charged such that the volume charge density is proportional to r
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