Net force in electric field determines charge

Steps:

• Initial free fall gives acceleration g, so mg is gravitational force.
• With pd applied (E = V/x upward on droplet): mg - qE = ma, so qE = m(g - a).
• Pd reversed (E downward): mg + qE = m a_max, so qE = m(a_max - g).
• Equate expressions for qE: g - a = a_max - g, and solve q = m(g - a)x / V.

Why A is correct:

• q = m(g - a)x / V derives directly from force balance, matching the simplified form in A assuming q_max and v encode m(g - a)x and V.

Why the others are wrong:

• B doubles the charge, ignoring the symmetric force addition/subtraction.
• C repeats A but contextually mismatches variable definitions.
• D identical to C, incorrect for same reason.

Final answer: A