TS EAMCET 03 May 2019 Shift 2 Solved Paper

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 ‌=‌

2kλ

x

=‌

2k

x

Similarly, for point charge,
E‌point charge ‌=‌

kq

(3−x)2

=‌

k

(3−x)2

‌‌...
From Eqs. (i), (ii) and (iii), we get
‌

2k

x

=‌

k

(3−x)2

⇒‌

2

x

=‌

1

(3−x)2

⇒‌‌2x2−13x+18=0
This is a quadratic equation, which have solution
x1,x2=‌

13±√132−144

4

So, x1=4.5m (not possible, as $0 Hence, the correct answer is 2m, which matches option (b).