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Question

Figure shows two equipotential lines in XY plane for an electric field. The scales are marked. The X-component Ex and Y-component Ey of the electric field in the space between these equipotential lines are respectively.


A
+100 Vm1, 200 Vm1
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B
+200 Vm1, +100 Vm1
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C
100 Vm1, +200 Vm1
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D
200 Vm1, +100 Vm1
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Solution

The correct option is C 100 Vm1, +200 Vm1

The parallel equipotential lines represent presence of a uniform Electric field in the region.

Electric field will be E perpendicular to the equipotential surfaces as shown in figure.

Slope of equipotential surfaces ,
tanθ=1042=12



sinθ=15 and cosθ=25

Here, potential difference ΔV=2 volt

Along the direction of Electric field.
Distance between two equipotential lines, d=0.02sinθ=0.25

Using, ΔV=Ed we have,

2=E×0.025

E=1005 V/m

From the geometry shown in figure ,
Ex=Esinθ=1005×15

Ex=100 V/m

similary ,
Ey=Ecosθ=1005×25

Ey=200 V/m

Hence, option (c) is the correct answer.
Why this question?

In such questions the parallel equipotential surface gives hint for uniform E, for which we can apply ΔV=Ed and distance between equipotential surface (d) in direction of E can be calculated by observing geometry.



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