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Chapter 12: Q12.42P (page 560)

Why can’t the electric field in Fig 12.35 (b) have a, z component? After all, the magnetic field does.

Short Answer

Expert verified

Because the electric filed generated by positive charge of the plate will get cancelled by the negative charge of the plate.

Step by step solution

01

Gauss law

The expression for the electric field is given by,

E→=σεo

HereE is the electric field,σ is the surface charge density andε0 is the permittivity of free space.

02

Explanation for the z component of the electric field.

Consider any point mid way between the sheets. For a positive charge sheet electric field is away from it and for a negative charge sheet electric field is towards it.

LetE→1zbe the electric field because of the small section of the positive plate and E→2zbe the electric field because of the small section of the negative plate.

As the magnitude of the surface charge density (σ) is same, thus from the Gauss law

|E1z|=|E2z|

But they will have opposite sign,

Ez,net=E→1z−E→2z=0

Therefore the zcomponent of the electric field is zero.

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