Two spherical shells have a common center. A -2.00 × 10-6 C charge is spread uniformly over the inner shell, which has a radius of 0.050 m. A +5.50 × 10-6 C charge is spread uniformly over the outer shell, which has a radius of 0.15 m.
To calculate the electric potential at a point between the two spherical shells, you can use the principle of superposition. This principle states that the electric potential at a point due to a collection of charges is equal to the algebraic sum of the electric potentials at that point due to each individual charge.
Step 1: Calculate the electric potential due to the inner shell
First, calculate the electric potential at the point of interest due to the charges on the inner shell. Since the charge is uniformly spread over the inner shell, we can consider the shell to be effectively a point charge located at its center.
The electric potential due to a point charge is given by the equation:
V = k * Q / r
Where:
V = electric potential at the point of interest
k = Coulomb's constant, approximately 9.0 × 10^9 N m^2/C^2
Q = charge
r = distance from the point charge to the point of interest
In this case, Q = -2.00 × 10^(-6) C and r = distance from the center of the inner shell (0.050 m) to the point of interest.
Step 2: Calculate the electric potential due to the outer shell
Next, calculate the electric potential at the point of interest due to the charges on the outer shell. Again, we can consider the outer shell to be effectively a point charge located at its center.
Using the same equation as before, the electric potential due to the charges on the outer shell is:
V = k * Q / r
Where:
V = electric potential at the point of interest
k = Coulomb's constant, approximately 9.0 × 10^9 N m^2/C^2
Q = charge
r = distance from the center of the outer shell (0.15 m) to the point of interest
In this case, Q = +5.50 × 10^(-6) C, and r = distance from the center of the outer shell (0.15 m) to the point of interest.
Step 3: Calculate the total electric potential
Finally, calculate the total electric potential at the point between the two shells by taking the algebraic sum of the potentials calculated in step 1 and step 2.
TotalV = V_inner + V_outer
Remember to consider the sign conventions for charges: positive charges will have positive potentials, and negative charges will have negative potentials.
This calculation will give you the electric potential at the point of interest between the two spherical shells.