I I\'m reposting this question as nobody gave the correct answer. The book answe

Question

I

I'm reposting this question as nobody gave the correct answer. The book answer is 4.33k q2/a2. Four point charges are at the corners of a square of side a as shown in the Figure. Determine the magnitude and direction of the resultant electric Force on q, with k e , q, and a left in symbolic form. Upper right hand corner: q (picture shows q) Upper left hand corner: Use 2q for calculations (although figure shows B) Lower right hand corner: 2q (although figure shows B) Lower left hand corner: 3q (although figure shows C) Please show all algebra, and feel free to provide additional rational as relates to understanding this problem.

Explanation / Answer

q(1)------------q(2)
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q(3)------------q(4)

the force on charge say q(2) due to 1 & 4 are equal and is k*2q*q/(a^2).they act perpendicularly
the resultant is 2^(1/2)*(k*2q*q/(a^2)).

the force due to the charge 3 is k*3q*q/((2^(1/2))*a)^2.

add both the forces.

= 2^(1/2)*(k*2q*q/(a^2)) + k*3q*q/((2^(1/2))*a)^2

= ((k * 2q^2 * 2^0.5 * 2)/ (2*a^2)) + (k*3q^2 / (2*a^2))

= ((k * 4q^2 * 2^0.5) / (2*a^2)) + (k*3q^2 / (2*a^2))

= ((k * 5.66q^2) / (2*a^2)) + (k*3q^2 / (2*a^2))

= (k*8.66q^2 / (2*a^2))

= k*4.33q^2 / a^2

= 4.33k q^2 / a^2

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