One plate of a capacitor is connected to a spring.Area of both the pla...
Explanation of the Force Constant of the Spring:
- Initial Configuration:
- Initially, when the capacitor is uncharged, the separation between the plates is d.
- The force between the plates is zero, as there is no electric field.
- Charged Configuration:
- When the capacitor is charged, in steady state, the separation between the plates decreases to 0.8d.
- This results in an electric field between the plates, causing a force on the charges.
- Force Acting on the Plates:
- The force acting on each plate of the capacitor is given by F = qE, where q is the charge on the plate and E is the electric field between the plates.
- Relation between Force and Spring Constant:
- The force acting on the plates of the capacitor is also the force acting on the spring when the plates are connected to it.
- This force causes a displacement in the spring, leading to the spring force kx, where k is the force constant of the spring and x is the displacement.
- Equilibrium Condition:
- At equilibrium, the forces due to the electric field and the spring are equal.
- Therefore, qE = kx, where qE is the force due to the electric field and kx is the spring force.
- Calculation of Force Constant:
- From the equilibrium condition, we can determine the force constant of the spring as k = qE/x.
- Substituting the values of q, E, and x in the equation will give us the force constant of the spring.