Parallel dielectrics in a capacitor

If three dielectric of slabs of same thickness, but different areas of  cross section A₁, A₂ & A₃ , dielectric constants K₁, K₂ & K₃ are placed between the plates of a parallel plate capacitor as shown, then the combination behaves as different dielectrics dividing the plate area are considered as capacitors connected parallel.

Capacitance of this is given by

C_net = C₁ + C₂ + C₃

^Uses of dimensions

• Correctness of a physical relation can be checked dimensionally. If dimensions of both the sides are found to be same, then the relation is said to be correct otherwise incorrect.
• Dimension of unknowns can be calculated.
• A mathematical relation between two or three quantities (called a physical relation) can be derived.
• Two different system of units can be interrelated.

Electrostatic field

If the electric field of a charge at a point doesn’t vary with the time, then the electric field is called electrostatic electric field. It’s effect on other charges is studied by defining two quantities; one a scalar field function called electric field potential ‘V’ & second a vector field function called electric field intensity  are related as

Here the –ve sign implies that electric field intensity due to both positive & negative charged configuration is always in the direction of decreasing field potential i.e. from a region of high potential to a region of low potential.