Question

Consider the situation shown in figure. The width of each plate is b. The capacitor plates are rigidly clamped in the laboratory and connected to a battery of emf V. All surface are frictionless. Calculate the extension in the spring in equilibrium (spring is nonconducting).

Answer 1

this particular case the electricfield attracts the dielectric into the capacitor with a force

$\frac{{\epsilon }_{0}b{V}^2(k-1)}{2d}$

b – Width of plates

k – Dielectric constant

d – Separation between plates

V = E = Potential difference.

this case the surfaces are frictionless, this force is counteracted by the weight.

$\frac{{\epsilon }_{0}b{E}^2(k-1)}{2d}=Mg$

$M=\frac{{\epsilon }_{0}b{E}^2(k-1)}{2dg}$