Respuesta :
There are two forces acting on the proton, the electrostatic force and the weight; we also know that the forces are balanced which means that they have to be equal, then we have:
[tex]\begin{gathered} F_e=W \\ \text{ where} \\ F_e\text{ is the electrostatic force} \\ W\text{ is the weight} \end{gathered}[/tex]Now, we know that the electrostatic force is related to the electric field by:
[tex]F_e=qE[/tex]and that the weight is given by:
[tex]W=mg[/tex]Plugging these in the first equation we have:
[tex]\begin{gathered} qE=mg \\ E=\frac{mg}{q} \end{gathered}[/tex]The mass and charge of the proton are:
[tex]\begin{gathered} m=1.67\times10^{-27} \\ q=1.6\times10^{-19} \end{gathered}[/tex]plugging the values in the expression for the field we have:
[tex]\begin{gathered} E=\frac{(1.67\times10^{-27})(9.8)}{1.6\times10^{-19}} \\ E=1.02\times10^{-7} \end{gathered}[/tex]Therefore, the magnitude of the field is:
[tex]E=1.02\times10^{-7}\text{ }\frac{N}{C}[/tex]Since a proton has a positive charge it will move in the direction of the field; in this case we need the force to be pointing up since the weight points down.
Therefore, the direction of the field is up.
