What is the magnitude of the electric field in which the electric force on a proton (mass 1.67×10^-27 kg, charge 1.60×10^-19 C) is equal to its weight?

• A. 5.0×10^-7 N/C
• B. 2.0×10^-7 N/C
• C. 1.02×10^-7 N/C
• D. 9.81×10^-7 N/C

Answer: (C)

Electric force on a charge in a field is F = qE, while weight is mg. If these forces have the same magnitude, qE = mg, so the field magnitude is E = mg/q.

Plug in m = 1.67×10^-27 kg, g ≈ 9.81 m/s^2, and q = 1.60×10^-19 C:

mg ≈ 1.67×10^-27 × 9.81 ≈ 1.64×10^-26 N.

E ≈ (1.64×10^-26 N) / (1.60×10^-19 C) ≈ 1.02×10^-7 N/C.

So the magnitude is 1.02×10^-7 N/C. Since the proton has a positive charge, the electric field would need to point upward to produce an upward electric force balancing the downward weight.