Question

A highly charged piece of metal (with uniform potential throughout) tends to spark at places where the radius of curvature is small, or at places where there are sharp points. The breakdown electric field strength for air is about 3 times 10⁶ V/m.

a) What is the maximum possible potential of a metal spheree of 2 cm radius in air? (That is, what is the potential at the surface of the spheree, relative to infinity?) _____volts
b) What is the maximum possible potential of a metal spheree of only 0.6 mm radius?____volts

Answer 1

The maximum possible potential of a metal sphere can be calculated using the formula V = Ed, where V is the potential, E is the electric field strength, and d is the distance.

Step-by-step explanation:

The maximum possible potential of a metal sphere with a radius of 2 cm can be calculated using the formula V = Ed, where V is the potential, E is the electric field strength, and d is the distance. Given that the breakdown electric field strength for air is 3x10^6 V/m, we can calculate the maximum potential as follows:

V = (3x10^6 V/m) * (2 cm) = 6x10^4 V = 60 kV

Similarly, for a metal sphere with a radius of 0.6 mm, the maximum potential can be calculated as:

V = (3x10^6 V/m) * (0.6 mm) = 1.8x10^3 V = 1.8 kV