Question

An infinite line charge produces a field of 18 x 1010
N/C at a distance of 1 m. The linear charge density
is
[NCERT Pg. 38]
(1) 10 C/m
(2) 2 x 10-1 C/m
(3) 2 x 10-2 C/m (4) 2 x 10-3 C/m​

Answer 1

Option:- (1) 10 μC/m

Electric field produced by the infinite line charges at a distance d having linear charge density λ is given by the relation,

$E \: = \frac{λ}{2πε0d}$

$λ \: = 2πε0dE$

where, d = 1 m

E = 18 × 10¹⁰ N/C

εo = Permittivity of free space and

1/4πεo = 9×10⁹ Nm²C-²

Therefore,

$λ = \: \frac{1 \times 18\times {10}^{10} }{2 \times 9 \times {10}^{9} }$

$λ = 10 \: μC/m$

Hence, the linear charge density is 10 μC/m.