Question

What is the magnitude of an electric field in which the electric force on a proton is equal in magnitude to its weight?Use 1.67×10−27 kg for the mass of a proton, 1.60×10−19 C for the magnitude of the charge on an electron, and 9.81 m/s2 for the magnitude of the acceleration due to gravity.

Answer 1

The electric force on the proton is:

F = Eq

F = electric force, E = electric field strength, q = proton charge

The gravitational force on the proton is:

F = mg

F = gravitational force, m = proton mass, g = gravitational acceleration

Since the electric force and gravitational force balance each other out, set their magnitudes equal to each other:

Eq = mg

Given values:

q = 1.60×10⁻¹⁹C, m = 1.67×10⁻²⁷kg, g = 9.81m/s²

Plug in and solve for E:

E(1.60×10⁻¹⁹) = 1.67×10⁻²⁷(9.81)

E = 1.02×10⁻⁷N/C

Answer 2

The magnitude of an electric field in which the electric force on a proton is equal in magnitude to its weight is; E = 1.024 × 10^-7 N/C

According to the question, the magnitude of the electric force is equal to its weight.

In essence;

• F(q) = Weight.

• However, F(q) = E × q

where;

• E = electric field magnitude

• q = charge on an electron.

Therefore;

• E × q = m × g

• E = (1.67 × 10^-27 × 9.81)/1.60× 10^-19

• E = 1.024 × 10^-7 N/C

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