Question

A proton is suspended in the air by an electric field at the surface of Earth. What is the strength of this electric field?

Answer 1

The strength of the electric field is
`1.02*10^(-7)(N)/(C)`

Step-by-step explanation:

By Newton's first law
`\sum\overrightarrow{F}=0` tells us that to maintain suspended the proton (at rest), the net force on it should be zero, assuming there's only gravitational interaction between earth and proton we should apply a force in the opposite direction equal to the weight of the proton (
`W=mg`, at earth surface) to make net force zero.

So, the electrostatic force on the charge should be:

`F_(e)=mg` (1)

with m the mass and g the gravity

but electrostatic force of a charge on an electric field is:

`F_(e)=Eq` (2)

with E the magnitude of electric field and q the charge of the proton

Equating (1) and (2):

`Eq=mg`

Solving for E:

`E=(mg)/(q)`

A fast search on google give us the mass of the proton and its charge:

`E=((1.67*10^(-27)kg)(9.81(m)/(s^(2))))/(1.60*10^(-19)C)=1.02*10^(-7)(N)/(C)`