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  • Infinite number of point charges <img alt="\mathrm{ q, \frac{q}{2}, \frac{q}{4}, \ldots . \infty}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%20q%2C%20%5Cfrac%7Bq%7D%7B2

Infinite number of point charges \mathrm{ q, \frac{q}{2}, \frac{q}{4}, \ldots . \infty} are placed on a non-conducting ring of radius \mathrm{R}. If it rotates with an angular speed \mathrm{\omega}, The equivalent current will be -
 

Option: 1

\mathrm{\frac{q}{\pi}}
 


Option: 2

\mathrm{\frac{q}{\pi \omega}}
 


Option: 3

\mathrm{\frac{q}{\omega}}
 


Option: 4

\mathrm{\frac{q \omega}{\pi}}


Answers (1)

best_answer

Use, \mathrm{\quad a=q+\frac{q}{2}+\frac{q}{4}+\cdots \infty}       ----------(1)

This is gemoterical series -

First term \mathrm{(a)=q, \quad r=\frac{q}{2} \times \frac{1}{q}=\frac{1}{2}}

\mathrm{ S_{\infty}=\frac{a}{1-r} }

from (1), \mathrm{ \quad S_{\infty}=\frac{q}{1-1 / 2}=2q }

current \mathrm{ \quad i=\frac{Q}{T}=\frac{2 q}{2 \pi / \omega} }

\mathrm{ i=\frac{q \omega}{\pi} }

Hence option 4 is correct.
 

Posted by

Ritika Kankaria

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