Question

Two spherical shells have a common center. The inner shell has Part radius R₁ =5.00 cm and charge q₁​ =+5.00×10⁻⁶ C; the outer shell has radius R₂ =15.0 cm and charge q₂ =−7.00×10⁻⁶ C. Both charges are spread uniformly over the shell surface. Take V=0 at a large distance from the shells. What is the electric potential due to the two shells at the distance r=2.50 cm from their common centec.

Answer 1

The electric potential at r = 2.50 cm from the center of two spherical shells with a common center is 8.9875 kV, calculated using the formula for the electric potential of a spherical charge distribution.

Step-by-step explanation:

The student's question involves determining the electric potential at a point due to two spherical shells with a common center. Since the point in question, r = 2.50 cm, is within the inner shell, only the charge on the inner shell affects the electric potential at that point. According to the principle of superposition and the properties of a conductor, the charge on the outer shell does not influence the electric potential inside it. The formula to calculate the potential due to a spherical charge distribution at a point r from the center inside the sphere is V = kq/R, where k is Coulomb's constant, q is the charge on the sphere, and R is the radius of the sphere. In this case, the electric potential at r = 2.50 cm is caused by the inner shell with charge q1 = +5.00 × 10−6 C and radius R1 = 5.00 cm.

Using Coulomb's constant k = 8.9875 × 109 Nm2/C2, the potential V at 2.50 cm from the center is calculated as follows:

V = k × q1 / R1 = 8.9875 × 109 × 5.00 × 10−6 / 0.05 m = 8.9875 × 103 V/m.

Therefore, the electric potential at the point r = 2.50 cm is 8.9875 × 103 volts or 8.9875 kV.