JEE Mains · Physics · STD 12 - Electric charges and fields
- JEE Mains 2021
- Medium
- Numerical
An infinite number of point charges, each carrying \(1 \,\mu C\) charge, are placed along the y-axis at \(y=1\, m , 2\, m , 4 \,m , 8\, m \ldots \ldots \ldots \ldots \ldots\) The total force on a \(1 \,C\) point charge, placed at the origin, is \(x \times 10^{3}\, N\). The value of \(x\), to the nearest integer, is ......... [Take \(\left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \,Nm ^{2} / C ^{2}\right]\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(12\)
Step-by-step Solution
Detailed explanation
\(F=k(1 C)(1 \mu C)\left[1+\frac{1}{2^{2}}+\frac{1}{4^{2}}+\frac{1}{8^{2}}+\ldots\right]\)
\(=9 \times 10^{3}\left[\frac{1}{1-\frac{1}{4}}\right]=12 \times 10^{3}\, N\)
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