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
This is what I get.
Explanation:
For an infinite non-conducting plane sheet located perpendicular to the
#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
#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
#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#