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Question

Two spheres of radii 12cm and 16cm have equal charges.The ratio of their energies is :


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Solution

Step 1: Given data

r1=12cmr2=16cm

Here,

r1 is the radius of the first sphere.

r2 is the radius of the second sphere.

Step 2: Formulation

Capacitance

  1. Capacitance is defined as the ratio of change in electrical charge to the change in potential of the system.
  2. The capacitance of a spherical object can be written as follows R:

C=4πε0r

Here, C is the capacitance, r is the radius of the sphere, and ε0 is the constant.

Hence, capacitance is directly proportional to the radius of the sphere.

3. The equation for the energy can be written as follows:

E=Q22CE=Q28πε0r

Here, E is the energy and Q is the charge.

Hence, energy is inversely proportional to capacitance.

Step 3: Calculation

Since both the spheres have equal charges, the relation between the energy and the radius can be written by combining the equation as follows:

E1rE1E2=r2r1E1E2=16cm12cmE1E2=43

Hence, the ratio of the energies of the spheres is 4:3.


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