Verified Solution • 2025–26 Session moderate

QJEEM21Pha211: JEE Main 2021 Physics - Class 12 JEEM21Pha211 Solution: Find out the surface charge density at the intersection of…

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.

Multiple Choice Options

  • A 0.424 nC m −- 2
  • B 4.0 nC m −- 2
  • C 47.88 C/m
  • D 0.07 nC m −- 2

Step-by-Step Verified Solution

Electric field due to wire is given by E=2kλrE = {{2k\lambda } \over r}

Electric field with surface charge density E=σ∈0E = {\sigma \over {{ \in _0}}}

2kλr=σ∈0{{2k\lambda } \over r} = {\sigma \over {{ \in _0}}}

⇒214π∈0λr=σ∈0\Rightarrow 2{1 \over {4\pi { \in _0}}}{\lambda \over r} = {\sigma \over {{ \in _0}}}

⇒82×3.14×3=σ\Rightarrow {8 \over {2 \times 3.14 \times 3}} = \sigma

⇒σ=0.424\Rightarrow \sigma = 0.424 n Cm −- 2

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