What is the electric potential at a height of #0.037m# above the plane if an infinite, non conducting plane with a surface charge density #sigma# is given by #+ 3.18 (pC)/m^2# (The potential at the surface of the plane 0 V.)?

1 Answer
A08
Mar 16, 2018

This is what I get.

Explanation:

For an infinite non-conducting plane sheet located perpendicular to the #y#-axis at #y=0#, having surface charge density #sigma# Electric field is given by the expression

#vecE=sigma/(2epsilon_0)hat j# for all points where #y>0#
where #epsilon_0=8.85 xx 10^-12 Fm^-1#, permittivity of free space.

Also electric potential at a point is given by

#V(y)=-int\ vecEcdotdvecy#

In the instant case we have only the #E_y#. Therefore we have

#V(y)=-int_0^y\ E_y\ dy=-(sigma/(2epsilon_0)y+C)#
where #C# is constant of integration.

Given that potential at the surface of plane #=0#
#=>V(y)=0" at "y=0#
#=>C=0#. Therefore, above expression becomes

#V(y)=-sigma/(2epsilon_0)y#

Inserting given values we get

#V(0.037\ m)=-(3.18xx10^-6)/(2xx8.85 xx 10^-12)xx0.037#
#=-6.647xx10^3\ V#

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