A spherical conductor has a radius of 14.0 cm and charge of 26.0 µC. Calculate the electric field and the electric potential (a) r = 10.0 cm, (b) r = 20.0 cm, and (c) r = 14.0 cm from the center.
Gauss law. Compute the total charge inside the "sphere" at the given radius r. Note, inside the sphere, you only have a fraction of the total charge.
E=kQ/r^2
The electric potential inside the sphere will be the same as it is on the surface so a=c. You can use the equation V=q/(4pi*8.89e-12*r) to find the potential where r is the radius from the center if that radius is greater than or equal to the radius of the sphere and q is the charge on the sphere. The electric field inside the sphere is zero. You can use the equation you supplied to find it elsewhere. Note this will only work for an enclosed sphere, meaning no holes in it.
To calculate the electric field and electric potential at different distances from the center of a spherical conductor, we need to use the formula for electric field and electric potential due to a charged sphere.
Formula for electric field due to a charged sphere:
E = k * (Q / r^2)
Formula for electric potential due to a charged sphere:
V = k * (Q / r)
Where:
E is the electric field (in N/C)
V is the electric potential (in V)
k is the Coulomb's constant (k = 8.99 x 10^9 Nm^2/C^2)
Q is the charge on the conductor (in C)
r is the distance from the center of the conductor (in m)
Now, let's calculate the electric field and electric potential at different distances from the center of the spherical conductor:
(a) r = 10.0 cm = 0.10 m
Using the given values, we can calculate the electric field and electric potential:
E = (8.99 x 10^9 Nm^2/C^2) * (26.0 x 10^-6 C) / (0.10^2 m^2)
V = (8.99 x 10^9 Nm^2/C^2) * (26.0 x 10^-6 C) / 0.10 m
(b) r = 20.0 cm = 0.20 m
Using the given values, we can calculate the electric field and electric potential:
E = (8.99 x 10^9 Nm^2/C^2) * (26.0 x 10^-6 C) / (0.20^2 m^2)
V = (8.99 x 10^9 Nm^2/C^2) * (26.0 x 10^-6 C) / 0.20 m
(c) r = 14.0 cm = 0.14 m
Using the given values, we can calculate the electric field and electric potential:
E = (8.99 x 10^9 Nm^2/C^2) * (26.0 x 10^-6 C) / (0.14^2 m^2)
V = (8.99 x 10^9 Nm^2/C^2) * (26.0 x 10^-6 C) / 0.14 m
Now, plug in the numbers and perform the calculations to find the electric field and electric potential at each distance.