Infinite number of charges of magnitude 6µ C each are lying at y = 2, 4, 8, 16 … metre on Y -axis. The value of electric field

Infinite number of charges of magnitude 6µ C each are lying at y = 2 4 8 16 … metre on Y -axis. The value of electric field intensity at point y = 0 due to these charges will be(a) 6.5 x 103 N / C(b) 4.05 x 104 N / C(c) 7.2 x 103 N / C(d) 1.8 x 104 N / C

Answer is : (d) 1.8 x 10 4  N / C The value of resultant electric field at y = 0 \(E=\frac{q}{4\pi \epsilon_0}\) \(\left[\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{8^2}+...\infty\right]\) = 6 x 10 -6 x 9 x 10 9 \(\left[\cfrac{\frac{1}{4}}{1-\frac{1}{4}}\right]\) = 54 x 10 3 x  \(\frac{1}{3}\) = 1.8 x 10 4 N/C