Two charged thin infinite plane sheets of uniform surface charge density $\sigma_{+}$ and $\sigma_{-}$, where $\left|\sigma_{+}\right|>\left|\sigma_{-}\right|$, intersect at right angle. Which of the following best represents the electric field lines for this system.

JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Electrostatics

Two charged thin infinite plane sheets of uniform surface charge density

σ_{+}

and

σ_{-}

, where

∣ σ_{+} ∣ > ∣ σ_{-} ∣

, intersect at right angle. Which of the following best represents the electric field lines for this system.

(A)(see structure)
(B)(see structure)
(C)(see structure)
(D)(see structure)
✓ Correct

Answer: (D)

Solution

Each infinite sheet produces a uniform field of magnitude

\frac{σ}{2 ϵ _{0}}

directed perpendicular to itself, pointing away from the positively charged sheet and towards the negatively charged one. With the two sheets crossing at right angles, the field in any region is the vector sum of these two mutually perpendicular uniform fields, so the lines run obliquely across each quadrant, beginning on the positive sheet and ending on the negative one. Because

∣ σ_{+} ∣ > ∣ σ_{-} ∣

the positive sheet's field is the stronger of the two, so the resultant lines are pulled round towards, and crowd more densely near, the positive sheet rather than sharing the quadrants symmetrically. The diagram showing this asymmetric, obliquely crossing pattern with denser lines about the more strongly charged sheet is the correct one.

JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Single correct option

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JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Electrostatics

Solution

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