When two conductors touch and have different sizes, how does charge distribute?

When two conductors touch and have different sizes, how does charge distribute?

• A. Both have the same charge
• B. Larger object has more charge
• C. Charge distributes so both have the same voltage, but larger has more charge
• D. No charge exchange

Answer: (C)

When conductors are connected, charges move so that the electric potential is the same everywhere along the connected conductors. The total charge is conserved, so the sum of the charges on both objects remains the same. If one conductor has capacitance C1 and the other C2, the common potential is V, and their charges are q1 = C1 V and q2 = C2 V. The total charge Q = q1 + q2 = (C1 + C2) V, so V = Q/(C1 + C2). Because capacitance grows with size, the larger object has a bigger C, and for the same V it must carry more charge: q1 > q2 if C1 > C2. So after touching, both objects share the same voltage, but the larger object holds more charge. If they were identical, they'd share charge equally.

When conductors are connected, charges move so that the electric potential is the same everywhere along the connected conductors. The total charge is conserved, so the sum of the charges on both objects remains the same.

If one conductor has capacitance C1 and the other C2, the common potential is V, and their charges are q1 = C1 V and q2 = C2 V. The total charge Q = q1 + q2 = (C1 + C2) V, so V = Q/(C1 + C2). Because capacitance grows with size, the larger object has a bigger C, and for the same V it must carry more charge: q1 > q2 if C1 > C2.

So after touching, both objects share the same voltage, but the larger object holds more charge. If they were identical, they'd share charge equally.