Air becomes a conductor when the electric field strength exceeds 3.00 × 106 N/C. Determine the maximum amount of charge that can be carried by a metal sphere 8.5 m in radius. The value of the Coulomb constant is8.99×109 N·m2/C2.

Answer in units of C.
I have the equations E=F/q and F=kq/r^2 but I'm not sure when to use either one.

To determine the maximum amount of charge that can be carried by a metal sphere, we can use the formula for electric field strength (E) in terms of charge (q) and distance (r).

The formula for electric field strength is:

E = k * q / r^2

Where:
E is the electric field strength
k is the Coulomb constant (8.99 × 10^9 N·m^2/C^2)
q is the charge
r is the radius of the metal sphere

Given that the electric field strength required for air to become a conductor is 3.00 × 10^6 N/C, we can set up the following equation:

3.00 × 10^6 N/C = (8.99 × 10^9 N·m^2/C^2) * q / (8.5 m)^2

Simplifying the equation:

3.00 × 10^6 N/C = (8.99 × 10^9 N·m^2/C^2) * q / 72.25 m^2

To find q, we can rearrange the equation and solve for it:

q = (3.00 × 10^6 N/C) * (72.25 m^2) / (8.99 × 10^9 N·m^2/C^2)

Calculating the expression:

q = (3.00 × 10^6 N/C) * (72.25 m^2) / (8.99 × 10^9 N·m^2/C^2)

q ≈ 0.0243 C

Therefore, the maximum amount of charge that can be carried by a metal sphere with a radius of 8.5 m is approximately 0.0243 Coulombs.

To determine the maximum amount of charge that can be carried by a metal sphere, we need to consider the condition when air becomes a conductor. This occurs when the electric field strength exceeds 3.00 × 10^6 N/C.

The electric field strength (E) is given by the equation E = F/q, where F is the force and q is the charge. In this case, we want to rearrange the equation to solve for the charge (q).

Rearranging the equation, we get q = F/E.

Next, we need to find the force (F) acting on the sphere. The force between two charges is given by the equation F = k * (q1 * q2) / r^2, where k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.

In this case, the charge q1 refers to the charge on the metal sphere, and q2 refers to the charge causing the electric field. Since we are interested in the maximum amount of charge that can be carried by the metal sphere, we let q1 be the charge we want to find.

Assuming the charge causing the electric field is far away from the sphere, we can consider it to be a point charge. Thus, the distance (r) between the charges will be twice the radius of the sphere.

Substituting these values into the equation, we get:

F = k * (q1 * q2) / (2r)^2

Now, we can substitute the known values into the equation:

F = (8.99 × 10^9 N·m^2/C^2) * (q1 * q2) / (2 * 8.5 m)^2

Since we are interested in the maximum amount of charge that can be carried by the sphere, we want to consider the case when the force (F) reaches the limit, which is when the electric field strength exceeds 3.00 × 10^6 N/C. So, we can set F = 3.00 × 10^6 N/C and solve for q1.

3.00 × 10^6 N/C = (8.99 × 10^9 N·m^2/C^2) * (q1 * q2) / (2 * 8.5 m)^2

Simplifying the equation, we solve for q1:

q1 = (3.00 × 10^6 N/C) * (2 * 8.5 m)^2 / (8.99 × 10^9 N·m^2/C^2 * q2)

Now, we can substitute the known values and solve for q1:

q1 = (3.00 × 10^6 N/C) * (2 * 8.5 m)^2 / (8.99 × 10^9 N·m^2/C^2 * q2)

Note: The value of q2 is not provided in the question, so without that information, we cannot determine the exact value of q1. However, using the given equations and steps above, you can calculate the value by substituting the appropriate values for q2.

Neither. We're talking fields not forces.

E = kq/r^2 or rearranged:
q=Er^2/k
Plug 'n' chug.