Question

kq1q2 k102f. Coulomb's Law is an empirical law. Through experiment, one can see that as the product of the two charges increases, the force between them increases. Further, if the separation between the charges increases, the Coulomb force between them decreases. But unlike the gravitational force between two masses, the Coulomb force can be either attractive or repulsive Theoretical Activi Consider the figure of a hanging charge (mass) on a string, and a prod with a charge of the same sign held close to it. Notice how the hanging charge repels Draw a force diagram representing all the forces acting on the mass, m. Draw the force diagram to scale with graph paper provided Referring to Fig. 1, show that the magnitude of the Coulomb force can be expressed as 1. 2. Coulomb-mg tan θ. 3. Refer to Fig. 2. Derive an equation relating tan θ as a function ofx and L. To do this, start by assuming a small angle approximation tan θ ~ sin θ. This assumes y L and that x « L. 772

Answer 1

Problem-1

The cosine component of the tension in the string will balance gravitational force whereas the sine component will balance coulomb's force.

The free body diagram mentioning all the forces is given below.

T-Tension T cos theta T Sin thetaCoulomb's Force mg

Problem-2

Thus by equating forces, we get

$T Cos \theta = m.g$

or

$T = \frac {mg}{cos \theta}$ eq-1

and

$F _{coulomb} = Tsin \theta$ eq-2

by putting the value of T from eq-1 into equation-2, we get

$F _{coulomb} = (\frac{mg}{cos \theta})sin \theta$

$F _{coulomb} = mg Tan \theta$ (Hence prooved)

Problem-3

In firgure 2 in the triangle

$sin \theta = \frac{x}{L}$

because theta is very small thus

$tan \theta = \frac{x}{L}$$sin \theta = \approx tan \theta = \frac{x}{L}$

by putting the value of tan theta in the forces equation, we get the value of foce in terms of x and L

thus

$F_{coulomg } = \frac{m.g.x }{L}$