Final answer:
The electric potential at point P depends on the distance r. If r is less than r1, the potential is kq1/r1; for r between r1 and r2, it's kq1/r; and for r greater than r2, the total potential is the sum kq1/r + kq2/r.
Step-by-step explanation:
The question involves finding the electric potential at a point P located at a distance r from the center of two concentric conducting spheres. When dealing with an electric potential problem in electrostatics, particularly with conducting spheres and point charges, it is crucial to consider whether the observation point is inside or outside the charged objects. The principles used to solve such a problem involve Gauss's law for electricity and the concept of superposition.
To find the electric potential at point P, we must consider the following scenarios:
- If r is less than r1, the electric potential due to the inner sphere is kq1/r1 as the potential is constant within a conductor, and there is no contribution from the outer sphere as it is shielded by the inner one.
- If r is between r1 and r2, that is r1 < r < r2, any charge on the outer sphere again has no effect due to shielding, and the potential at P is still due to the inner sphere, so it remains kq1/r.
- Lastly, if r is greater than r2 (outside the outer sphere), the potential at P is the sum of the potentials due to both spheres which can be expressed as kq1/r + kq2/r because the potential outside a spherical charge distribution is equivalent to that of a point charge located at the center.
The constant k is the Coulomb's constant, and it is essential in calculating electrostatic forces and potentials. Hence, to get the electric potential at point P, you need to apply the correct scenario based on the distance r.