Answer to Question #138229 in Mechanics | Relativity for Gasty

Question

Four charged particles are at the corners of a square of side a. Determine (a) the electric field at the location of charge q and (b) the total electric force exerted on q.

Answer 1

q is the charge

a is the (magnitude) which is then squared

for $A_q,$ $E=\frac{ke\times3q}{a^{2}}\times [cos(0), 0]$ ,

$B_{q}, E= \frac{ke\times4q}{2a^{2}}\times[ cos45, sin45]$

$C_{q}, E=\frac{ke\times3q}{a^{2}}\times[0, sin90]$

i like using (i and j instead of x and y). Sum of the electric fields is

$E_{q} = \frac{ke\times q}{a^{2}}\times(3i + (4cos45)i + 4sin45j + 3j$

$\frac{ke\times q }{a^{2}}\times(5.828i + 5.828j)$

$\frac{ke\times q }{a^{2}}\times8.24$

$tan\theta = \frac{opposite}{adjacent}= \frac{5.828}{5.828}=1$

$tan^{-1}1=45^{0}$

(b) The total electric force on q is $\frac{ke\times q }{a^{2}}\times(8.28)$ at an angle of $45^{o}$