This problem is similar to and this problem was solved like this So, can the fir

Question

This problem is similar to

and this problem was solved like this

So, can the first image be solved using the similar method? I tried it myself but don't understand where the 3/2 is coming from or if it's just limited to the similar problem. Only thing different between the two is the numbers used.

Four charged particles are at the corners of a square of side a as shown in the figure below. (Let A B 4, and C 7.) Aq Bay (a) Determine the electric field at the location of charge q. (Use the following as necessary: q, a, and ke.) magnitude direction o counterclockwise from the +x-axis) (b) Determine the total electric force exerted on q. (Use the following as necessary: q, a, and ke.) magnitude direction o counterclockwise from the +x-axis)

Explanation / Answer

as we know that the electric field

E = kq / r2

on 5q charge

E1 = Kq1 / r12

= 9 x 109 x 5q / a2  = ( 45 x 109 x q ) / a2

on 4q charge

E2 = kq2 / r22

= ( 9 x 109 x 4q ) / (root2 x a) 2

= (18 x 109 x q) / a2

on 7q charge

E3 = Kq3 / r32

= ( 9 x 109 x 7q ) / a2   

= ( 63 x 109 x q ) / a2

so the total electric field

E = E1 + E2 + E3

= ( 126 x 109 x q ) / a2 N / C Ans

direction is given by

= i + ( j sin45 + i cos 45 ) + i

= 2.707 i + 0.707 j

so angle   

Q = tan-1(0.707 / 2.707)

= 14.63o   Ans

(b) the total electric force is given by

F = qE

= ( q x 126 x 109 x q ) / a2

= (126 x 109 x q2 ) / a2  N Ans

the direction is same as the electric field

so direction = 14.63o   Ans

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