What voltage 4.5 cm away from the center of a metal sphere of radius 3.5 cm would produce a static charge of 2.2 μC?

The voltage V at a distance r from the center of a sphere carrying a charge Q is given by the formula:

V = kQ/r

where k is Coulomb's constant, which is approximately 8.99 x 10^9 N m^2/C^2.

In this case, the charge Q is 2.2 μC, which is 2.2 x 10^-6 C. The distance r is 4.5 cm, which is 4.5 x 10^-2 m.

Substituting these values into the formula gives:

V = (8.99 x 10^9 N m^2/C^2) * (2.2 x 10^-6 C) / (4.5 x 10^-2 m)

Solving this equation gives the voltage at a distance of 4.5 cm from the center of the sphere.

The electric potential (V) due to a point charge is given by the formula:

V = kQ/r

where:

• V is the electric potential (voltage),
• k is Coulomb's constant (8.99 x 10^9 N.m^2/C^2),
• Q is the charge (in this case, 2.2 μC = 2.2 x 10^-6 C), and
• r is the distance from the point charge (in this case, 4.5 cm = 0.045 m).

Substituting the given values into the formula, we get:

V = (8.99 x 10^9 N.m^2/C^2) * (2.2 x 10^-6 C) / 0.045 m

Solving this equation will give us the voltage 4.5 cm away from the center of the metal sphere.

The electric potential (voltage) V at a distance r from the center of a sphere carrying a charge Q is given by the formula:

V = kQ/r

where k is Coulomb's constant, approximately 8.99 x 10^9 N m^2/C^2.

In this case, the charge Q is 2.2 μC = 2.2 x 10^-6 C, and the distance r is 4.5 cm = 0.045 m.

Substituting these values into the formula gives:

V = (8.99 x 10^9 N m^2/C^2) * (2.2 x 10^-6 C) / 0.045 m

Solving this equation gives:

V = 4.4 x 10^5 Volts

So, the voltage 4.5 cm away from the center of the sphere would be 440,000 Volts.