Question

One picocoulomb of charge is distributed on a
ring of diameter 1 mm. The potential at the
centre of the ring is:
A. Zero
B. 18 volt
C. -18 volt
D. -14.4 volt​

Answer 1

Answer:

14.4 volt.

Explanation:

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Answer 2

The potential difference at the center of the ring will be (B) 18 volt.

Given:

Charge on the ring $=1 pico$ $C$

Diameter of the ring $=1mm$

To find:

The potential at the center of the ring.

Solution:

The electric potential at any point of an object is the work done in bringing a charge from infinity to the point on which the potential is to be calculated.

Mathematically,      $V=\frac{W}{q}$

We know,

Ring is an open object and the potential inside an open object cannot be zero. Considering a charged ring of diameter $d$, each element of the ring will act as a potential charge that will attract or repel the incoming test charge.

Hence, this potential at the center of the ring of radius $R$ will be

$V=\frac{1}{4\pi E_{o} } \frac{Q}{R}$

The radius of the ring will be

$R=\frac{d}{2}=\frac{1mm}{2}=0.5mm=0.5$ × $10^{-3}m$

Charge $Q= 1$ × $10^{-12} C$

$V=\frac{9*10^{9}*1*10^{-12} }{0.5*10^{-3} }$

$V=\frac{9*10^{-3} }{0.5*10^{-3} }$

$V=18V$

Final answer:

Hence, the potential difference at the center of the ring will be (B) 18 volt.