SATHEE: Electrostatics 2 Question 15

Electrostatics 2 Question 15

16. A non-conducting ring of radius $0.5 m$ carries a total charge of $1.11 \times 10^{- 10} C$ distributed non-uniformly on its circumference producing an electric field $E$ everywhere in space. The value of the integral $\int_{l = \infty}^{l = 0} - E \cdot d l (l = 0$ being centre of the ring) in volt is

(1997, 2M)

(a) +2

(b) -1

(d) zero

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Answer:

Correct Answer: 16. (a)

Solution:

$- \int_{l = \infty}^{l = 0} E \cdot d l = \int_{l = \infty}^{l = 0} d V = V$ (centre) $- V$ (infinity)

but $V$ (infinity) $= 0$

$∴ - \int_{l = \infty}^{l = 0} E \cdot d l$ corresponds to potential at centre of ring.

and $V ($ centre $) = \frac{1}{4 π ε_{0}} \cdot \frac{q}{R}$

$= \frac{(9 \times 10^{9}) (1.11 \times 10^{- 10})}{0.5} \approx 2 V$

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Electrostatics 2 Question 15

16. A non-conducting ring of radius 0.5 m carries a total charge of 1.11×10−10C distributed non-uniformly on its circumference producing an electric field E everywhere in space. The value of the integral ∫l=∞l=0−E⋅dl(l=0 being centre of the ring) in volt is

Answer:

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