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JIPMER 2017
Exam
JIPMER
Year
2017
Subject
Physics
Chapter
Electrostatics

JIPMER 2017 · Physics · Electrostatics

A non-conducting ring of radius 0.5 m carries a total charge of...

A non-conducting ring of radius 0.5 m carries a total charge of 1.11×10−10C1.11 \times 10^{-10} \mathrm{C} distributed non-uniformly on its circumference producing on its circumference on electric field E\mathbf{E}, everywhere in space. The value of the line integral ∫l=∞l=0(−E⋅dl)\int_{l=\infty}^{l=0}(-\mathbf{E} \cdot \mathbf{d l}) (l=0(l=0 being centre of ring) in volts is

Options

  1. A+2+2
  2. B−1-1
  3. C−2-2
  4. DZero

Correct answer

A. +2+2

Step-by-step solution

From definition of potential difference ∫l=∞l=0E⋅dl=\int_{l=\infty}^{l=0} \mathbf{E} \cdot \mathbf{d l}= potential difference at infinity and at centre of ring =Vcentre −Vinfinity =V_{\text{centre }}-V_{\text{infinity }} But by convention Vinfinity =0V_{\text{infinity }}=0 and Vcentre =14πε0qR=9×109×1⋅11×10−100.5=2volt∴∫l=∞l=0(−E⋅dl)=2V_{\text{centre }}=\frac{1}{4 \pi \varepsilon_0} \frac{q}{R} =9 \times 10^9 \times \frac{1 \cdot 11 \times 10^{-10}}{0.5}=2 \mathrm{volt} \therefore \int_{l=\infty}^{l=0}(-\mathbf{E} \cdot \mathbf{d l})=2 volt -0 volt =2=2 volt
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