An infinite line of uniform charge density is placed along
y -axis and a charge
(+1C) is placed at
x=+3m, as shown in the figure. For electric field to be zero at
x, there should be
E‌line charge ‌=E‌point charge ‌‌‌......(1)
As we know, for line charge
E‌line charge ‌=‌=‌ Similarly, for point charge,
E‌point charge ‌=‌=‌‌‌... From Eqs. (i), (ii) and (iii), we get
‌=‌⇒‌=‌ ⇒‌‌2x2−13x+18=0 This is a quadratic equation, which have solution
x1,x2=‌ So,
x1=4.5m (not possible, as $0
Hence, the correct answer is 2m, which matches option (b).