Question

Q6.  a) You put a uniformly shaped bit of dielectric material in between the plates of a plate capacitor. When you do this, the charge on each plate remains unchanged.

How does this affect the difference in potential between the two plates?

(A) The potential difference increases.

(B) The potential difference is not affected.

(C) The potential difference decreases.

Explain your reasoning.

b) Consider the same configuration as above. How does the dielectric material affect the energy stored in the capacitor?

(A) The stored energy increases.

(B) The stored energy does not change.

(C) The stored energy decreases.

Explain your reasoning.

c) Again, same configuration. Will there be an electrostatic force on the dielectric material when you put it in between the plates, and if so - what is the direction of the force?

(A) No electrostatic force is affecting the object.

(B) The object is affected by a force that pulls the object towards the area between the plates.

(C) The object is affected by a force that forces it away from the area between the plates.

Explain your reasoning.

______________________________________

Thank you in advance!

Answer 1

Q6 .a) Answer C : The potential difference decreases.

Inserting the dielectric material between the plates increases the capacitance of capacitor by    dimensionless factor k (dielectric constant), C = C₀ k

   By definition of capacitance C₀ = Q/dV_o, as inserting the dielectric the capacitance increases, the potential    difference must decreases which leads to increase in capacitance. Also the potential difference decreases    by same factor k, dv = dv₀/k

   b) Answer C : Stored energy decreases.

By definition U₀ = Q²/2C₀ as Q remains unchanged and C₀ increases by factor k so the energy decreases    by factor k.

   U = Q²/2C = Q²/2C₀k = U₀/k

   c) Answer B : The object is affected by a force that pulls the objects towards the area between the plates.

   In part b we have seen that energy decrease which leads to negative work done on dielectric. This means the force must pulls the object towards the area between the plate.

Non uniform electric field at the edge of the capacitors exerts force on the induced charges on the surface of the dielectrics.This field is referred as fringe field, and its horizontal component acts on the non uniform induced charges on the surface of the dielectrics which pulls dielectric inside.