Question

Two protons and an electron are placed on corners of a square with sides 9 cm. The electron is opposite the empty corner. Which of the following is the magnitude of the electric force on the electron? 2.84 x 10-26 N 3.62 x 10-27 N 0 N 4.02 x 10-26 N

Answer 1

see the diagram :

r TI te - е ' 7 te

given :

r = 9cm = 0.09 m

charge on electron = -e

charge on proton = +e

F = force exerted by proton on electron [since both protons are equidistant from electron, the magnitude of force exerted by the protons on electron is same]

$=\frac{ke^{2}}{r^{2}} = \frac{9*10^{9}*(1.6*10^{-19})^{2}}{0.09^{2}}=2.84*10^{-26}N$

Now, as the forces F are mutually perpendicular, the net force (according to parallelogram law of vector addition) is

= $\sqrt{2}F = \sqrt{2}*\frac{9*10^{9}*(1.6*10^{-19})^{2}}{0.09^{2}}=4.02*10^{-26}N$ [answer]

[correct option is option (d) ]