Question:

A spherical conductor with an initial charge of -12.0 microcoulombs is placed in a uniform electric field, resulting in a potential difference of 2000 V across its surface. The conductor is then connected to a conducting wire and an additional charge of +8.0 microcoulombs is added to the conductor. Calculate:

a) The electric field strength inside the conductor before connecting the wire. b) The final charge on the conductor after connecting the wire. c) The electric potential of the conductor after connecting the wire.

Answer:

a) To determine the electric field strength inside the conductor before connecting the wire, we can use the formula for electric field strength inside a conductor:

E_inside = -ΔV / d

Where E_inside is the electric field strength inside the conductor, ΔV is the potential difference across the conductor, and d is the distance across which the potential difference occurs.

Given: ΔV = 2000 V d = Diameter of the conductor

Since the conductor is spherical, the diameter is equal to the diameter of the conductor. Therefore, we can substitute the values into the equation:

E_inside = -2000 V / d (Equation 1)

b) To find the final charge on the conductor after connecting the wire, we can use the principle of charge conservation. The initial charge of the conductor is -12.0 microcoulombs, and an additional charge of +8.0 microcoulombs is added. The final charge can be calculated using the equation:

Final charge = Initial charge + Additional charge

Final charge = (-12.0 μC) + (8.0 μC) Final charge = -4.0 μC (since charges of opposite signs cancel each other out)

c) The electric potential of the conductor after connecting the wire is the same as the potential difference across its surface.

Therefore, the electric potential of the conductor after connecting the wire is 2000 V.

So, the final answers are:

a) The electric field strength inside the conductor before connecting the wire is given by Equation 1: E_inside = -2000 V / d.

b) The final charge on the conductor after connecting the wire is -4.0 microcoulombs.

c) The electric potential of the conductor after connecting the wire is 2000 V.