Consider three conducting spheres each 10 cm in diameter. “A” has a net charge of 5 C, “B” has a net charge of 10 C, and “C” has a net charge of zero, but is placed in an electric field of 1000 V/m. Rank the electric field strength inside the spheres from weakest to strongest.
To rank the electric field strength inside the spheres, we need to consider the relationship between the electric field and the charge distribution.
The electric field inside a conducting sphere is zero if there is no net charge inside the sphere. This means that the electric field inside sphere C will be zero.
For spheres A and B, the electric field inside depends on the charge distribution. The electric field inside a conducting sphere with a net charge is given by the equation:
E = kQ / r^2
where E is the electric field, k is Coulomb's constant, Q is the net charge, and r is the radius of the sphere.
Let's calculate the electric field inside spheres A and B using this equation:
For sphere A:
- Radius (r) = 10 cm = 0.1 m
- Net charge (Q) = 5 C
- Coulomb's constant (k) = 8.99 x 10^9 N m^2/C^2
E(A) = (8.99 x 10^9 N m^2/C^2)(5 C) / (0.1 m)^2
E(A) = 4.4945 x 10^12 N/C
For sphere B:
- Radius (r) = 10 cm = 0.1 m
- Net charge (Q) = 10 C
- Coulomb's constant (k) = 8.99 x 10^9 N m^2/C^2
E(B) = (8.99 x 10^9 N m^2/C^2)(10 C) / (0.1 m)^2
E(B) = 8.989 x 10^12 N/C
Now we can rank the electric field strength inside the spheres:
1. Sphere B with an electric field strength of 8.989 x 10^12 N/C.
2. Sphere A with an electric field strength of 4.4945 x 10^12 N/C.
3. Sphere C with an electric field strength of zero (no electric field present).
Therefore, the ranking of electric field strength inside the spheres from weakest to strongest is C, A, B.
To rank the electric field strength inside the spheres from weakest to strongest, we need to understand how electric field behaves inside conductors.
Inside a conductor that is in electrostatic equilibrium, the electric field is zero. This is because charges in a conductor will redistribute themselves in such a way that there is no net electric field inside.
Now, let's analyze each sphere separately:
1. Sphere A with a net charge of 5 C:
Since Sphere A has a net charge, it will create an electric field inside it. However, the electric field will not be uniform throughout the sphere. Instead, it will be strongest at the surface of the sphere and weaker towards the center. Therefore, we can say that the electric field inside Sphere A is non-zero but weaker than at the surface.
2. Sphere C with a net charge of zero but placed in an electric field of 1000 V/m:
In this case, there is no net charge on Sphere C. However, it is subjected to an external electric field of 1000 V/m. Inside a conductor, charges redistribute themselves in response to an external electric field. As a result, an induced charge will be created inside the conductor that will generate an electric field to counteract the external electric field. Inside Sphere C, the electric field will be opposite in direction but of the same magnitude as the external field, resulting in a zero net electric field inside.
3. Sphere B with a net charge of 10 C:
Similar to Sphere A, Sphere B will have a nonzero electric field inside because of its net charge. The strength of the electric field inside Sphere B will follow the same pattern as Sphere A, strongest at the surface and weaker towards the center. However, since the net charge of Sphere B is larger than that of Sphere A, the electric field inside Sphere B will be stronger than in Sphere A.
Therefore, we can rank the electric field strength inside the spheres from weakest to strongest as follows:
3. Sphere C (electric field strength is zero)
2. Sphere A (weaker electric field than Sphere B)
1. Sphere B (strongest electric field)