Three point charges qa, qb, and qc are situated at the vertices of an equilatera

Question

Three point charges qa, qb, and qc are situated at the vertices of an equilateral triangle of side length d. All Charges are positive and have the following magnitude relationship: qa = 2qb = Find the magnitude and direction of the electric field at the midpoint of the line joining qa and qb. Find the magnitude and direction of the electric field at the center of the triangle. Should there be a place (other than at infinity) where the electric field will be zero? (Note, you do not need to find this location if you say yes.)

Explanation / Answer

a ) Given that q_a , q_b , q_c vertices of equilateral triangle  

sides lenghth is d

magnitude of q _a and q_b

E = k q / r^2

    = k q_a / r ^2

r = d * ( 3/2 )

E_1 = 4 k q_a / 3d^2

E= [(E2+E3)^2+E1^2],..........(1)

b ) E2= E3= 2 kq/(d/2)^2     

           = 8 kq/d^2

substitute the values of E_1 &E_2 & E_3 in E   to get solution

c ) At the mid point , exactly half way between the two equal charges , the electric field is zero At that point the force on the third charge is zero . .

    

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