If the electric field strength in air is more than 3x106 N/C then the air will be become agood conductor .Determine the amount of charge that can be carried by a metal sphere of radius 2.0 m
apply E=kq/r^2
then you can directly find q
To determine the amount of charge that can be carried by a metal sphere, we need to use the formula for the capacitance of a sphere:
C = 4πε₀r
Where:
C is the capacitance of the sphere,
π is the mathematical constant pi (approximately 3.14159),
ε₀ is the permittivity of free space (approximately 8.85 x 10⁻¹² F/m),
and r is the radius of the sphere.
Given that the radius of the metal sphere is 2.0 m, we can substitute this value into the formula to find the capacitance:
C = 4π(8.85 x 10⁻¹²)(2.0)
C = 4π(17.7 x 10⁻¹²)
C ≈ 70.63 x 10⁻¹² F
The amount of charge (Q) that can be carried by the metal sphere can be calculated using the relationship between charge and capacitance:
Q = CV
Where Q is the charge, C is the capacitance, and V is the electric potential (or voltage) difference across the sphere. Since we are not given the voltage difference, we cannot determine the specific value of charge. However, we can still discuss the relationship between charge and capacitance.
The greater the capacitance, the more charge can be stored on the sphere for a given voltage difference. Therefore, the larger the capacitance of the sphere, the greater the charge it can carry.