# Two identically charged particles are fastened to the two ends of a spring of spring constant 100 N m–1 and natural length 10 cm. The system resets on a smooth horizontal table. If the charge on each particle is 2.0 × 10–8 C, find the extension in the length of the spring. Assume that the extension is small as compared to the natural length. Justify this assumption after you solve the problem.

Given:
Natural Length of the spring: l = 10cm = 0.1m
Spring Constant : K = 100 N m–1
Charge on each particle: q = 2.0 × 10–8 C
Separation between two charges = l
Formula used:
Let the extension be ‘x’ m.
We use Coulomb’s Law:
Where Fe is the electrostatic force, k is a constant .
k =
= 9× 109 Nm2C-2 and r is the distance between two charges.
Since the electrostatic force is repulsive in nature, the spring will exert a restoring spring force Fr.
F= -Kx

Here, K is the spring constant and x is the extension.
Negative sign is because the restoring spring force us opposite to the applied force. The system would be in equilibrium when the Electrostatic force of repulsion between the two charges is equal to the spring force

Fe + Fr = 0

Yes, the assumption is justified. When two similar charges are present at two ends, they will exert repulsive force on each other. The spring will extend due to its elastic nature.
The repulsive force will have an opposite force called as restoring force in the spring. This force is directly proportional to the extension of the spring and depends on the elasticity if the material. If the extension is large compared to the natural length, then the restoring force would be proportional to the high powers of the extension.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)47 mins
Check your knowledge of Electric Potential | Quiz45 mins
Relation between electric field and potential34 mins
Relation between Electric field & Potential45 mins
Interactive quiz on Relation between electric field and potential43 mins
Electric field inside cavity37 mins
Few Applications of Gauss's law54 mins
Electric potential inside solid and hollow sphere30 mins
Test Your Knowledge of Electric Charge & Coulomb's Law47 mins
Electric Field Lecture47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses