Two thin conductive spheres with radii of 10cm and 20cm are nested together so that their centers are at the same location. If the inner sphere has a net charge of 15 nC and the outer sphere has no net charge (quasi-neutral). What is the electric field at r=15cm between the two spheres and at r=30cm outside the outer sphere?
To find the electric field at a point, we can use Coulomb's Law, which states that the electric field due to a point charge is given by:
E = k * (Q / r^2)
Where E is the electric field, k is the Coulomb's constant (9 x 10^9 Nm^2/C^2), Q is the magnitude of the charge, and r is the distance from the charge.
In this case, we need to find the electric field at two different points:
1. Electric field at r = 15 cm (between the two spheres):
To calculate the electric field at this point, we need to consider the contribution of both spheres. The inner sphere has a net charge of 15 nC, and the outer sphere has no net charge. Hence, the inner sphere creates an electric field, while the outer sphere does not contribute.
Let's calculate the electric field due to the inner sphere first:
E_inner = k * (Q_inner / r_inner^2)
E_inner = (9 x 10^9 Nm^2/C^2) * (15 x 10^(-9) C) / (0.1 m)^2
E_inner = 1350 N/C
So, the electric field due to the inner sphere at r = 15 cm is 1350 N/C. Since the outer sphere has no net charge, it does not contribute to the electric field.
2. Electric field at r = 30 cm (outside the outer sphere):
To calculate the electric field at this point, we only need to consider the outer sphere since it is the only charge source.
E_outer = k * (Q_outer / r_outer^2)
E_outer = (9 x 10^9 Nm^2/C^2) * (0 C) / (0.3 m)^2
E_outer = 0 N/C
So, the electric field at r = 30 cm (outside the outer sphere) is 0 N/C as there is no net charge.
In summary:
- Electric field at r = 15 cm (between the two spheres) is 1350 N/C.
- Electric field at r = 30 cm (outside the outer sphere) is 0 N/C.