Question

Prove f=-dv/dx for conservative force.​​

Answer 1

Given:

f = - dv/dx

To find:

Prove f = - dv/dx for conservative force.​​

Solution:

We will prove the given equation using the electric field equation.

The electric field equation is given as follows.

E = - dФ/dx

where dФ/dx represents the change in the flux with respect to the distance in 2D.

We know the relation between the force and the electric field and in mathematically represented as follows.

F = qE

where q is the total amount of charge present and E is the electric field.

substitute the electric field equation in terms of the change in flux.

So, we get,

F = q (-dФ/dx)

where dФ is the electrostatic potential.  Thus, in the case of a conservative force, we can write,

dФ = dV

∴ F = - dV/dx

Hene it is proved that f = -dv/dx for conservative force.​​