JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Electrostatics

Find out the surface charge density at the intersection of point

x = 3 m

plane and

x

-axis, in the region of uniform line charge of

8 nC / m

lying along the

z

-axis in free space.

Answer: (A)

Solution

Take a coaxial cylindrical Gaussian surface of radius

r

and length

ℓ

about the line charge. The flux leaves only through the curved face, so

E (2 π r ℓ) = \frac{λ ℓ}{ε _{0}}

and the electric flux density is

D = ε_{0} E = \frac{λ}{2 π r}

directed radially outwards. The plane

x = 3 m

cuts the

x

-axis at a point lying

r = 3 m

from the

z

-axis, so

D = \frac{8 nC m ^{- 1}}{2 π \times 3 m} = \frac{8}{18.85} = 0.424 nC m^{- 2}

The charge density on a surface placed normal to the field at that point is

0.424 nC m^{- 2}

JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Single correct option