Potential at centre of annular ring of inner radius a and outer radius...
Electric Potential at the Center of an Annular Ring
Electric Potential, also known as voltage, is a scalar quantity that describes the electric potential energy per unit charge at a certain point in space. In the case of an annular ring with charge distributed on both rings, we can calculate the electric potential at the center of the ring using the principle of superposition.
Electric Potential Due to Inner Ring
- The electric potential at the center of the annular ring due to the inner ring can be calculated using the formula: V_inner = k * (Q_inner) / (b - a), where k is the Coulomb's constant, Q_inner is the charge on the inner ring, a is the inner radius, and b is the outer radius.
Electric Potential Due to Outer Ring
- Similarly, the electric potential at the center of the annular ring due to the outer ring can be calculated using the formula: V_outer = k * (Q_outer) / (b), where Q_outer is the charge on the outer ring.
Total Electric Potential
- The total electric potential at the center of the annular ring is the sum of the potentials due to the inner and outer rings: V_total = V_inner + V_outer.
- Substituting the values of V_inner and V_outer into the total potential formula gives: V_total = k * (Q_inner) / (b - a) + k * (Q_outer) / (b).
- This formula gives the electric potential at the center of the annular ring with charge Q uniformly distributed on both rings.