Question

What is the electric field strength at a point in space where a proton experiences an acceleration of 1.4 million "g's"?

Answer 1

The strength of the electric field is 0.143 N/C

Explanation:

The acceleration experienced by the proton is:

$a=1.4\cdot 10^6 g=(1.4\cdot 10^6)(9.8)=1.37\cdot 10^7 m/s^2$

where

$g=9.8 m/s^2$ is the acceleration of gravity

From Newton's second law, we know that the net force on the proton is

$F=ma$

where

$m=1.67\cdot 10^{-27} kg$ is the mass of the proton

$a=1.37\cdot 10^7 m/s^2$ is the acceleration

Substituting,

$F=(1.67\cdot 10^{-27})(1.37\cdot 10^7)=2.29\cdot 10^{-20} N$

And this is equal to the force exerted by the electric field on the proton, given by

$F=qE$

where

$q=1.6\cdot 10^{-19} C$ is the charge of the proton

E is the magnitude of the electric field

And solving for E, we find

$E=\frac{F}{q}=\frac{2.29\cdot 10^{-20}}{1.6\cdot 10^{-19}}=0.143 N/C$

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