What electric field strength is needed to balance the weight of a proton (mass 1.67×10^-27 kg, charge +e)?

• A. 1.02×10^-7 N/C upward
• B. 5.57×10^-11 N/C downward
• C. 1.02×10^-7 N/C downward
• D. 5.57×10^-11 N/C upward

Answer: (A)

Balance occurs when the electric force on the proton equals its weight: qE = mg. For a proton, q = +e, so the electric force is in the direction of the electric field. Since weight acts downward, the field must point upward to provide an upward electric force.

Compute the values: weight W = mg ≈ (1.67 × 10^-27 kg)(9.8 m/s^2) ≈ 1.64 × 10^-26 N. With q = e ≈ 1.60 × 10^-19 C, the required field is E = W/q ≈ (1.64 × 10^-26 N)/(1.60 × 10^-19 C) ≈ 1.02 × 10^-7 N/C.

Therefore, the needed electric field is about 1.02 × 10^-7 N/C upward.