Using the symmetry of the arrangement, determine the direction of the electric f

Question

Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square at the location of charge q in the figure below, given that qa = qb = –1.65 C and qc = qd = 1.65 C.

Calculate the magnitude of the electric field at the location of q, given that the square is 7.75 cm on a side.

Openstax College Physics presented by Sapling Leaming Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square at the location of charge q in the figure below, given that qa--1.65 C and down and right down O up and right O down and left O up upand left O right left Calculate the magnitude of the electric field at the location of q, given that the square is 7.75 cm on a side. Number 7.6× 105 N/C Previous Give Up & View Solution 0 Check Answer Next Exit Hint

Explanation / Answer

By symmetry the electric field at q will be added the resultant will be along the upper corners of the given square

and we knwo that the electric field direction of a positive charge is out ward or away from the charge and for negative charge the field direction is inward

so the electric field due to charges qa,qd is  

Ea,d is along the upper left corner and due to Eb,c is along the upper right corner

resolving the field vectors into the components we get the horizontal components were cancel because they were at equal distances from the charge q and of equal in magnitude , only the y components will remain

E = kq_b(2/r^2) sin 45+k*q_c(2/r^2) sin 45 + k*q_a(2/r^2) sin135+k*q_d(2/r^2) sin135

E = 9*10^9*2*(1.65*10^-6)(4/0.0775^2)sin 45 + 9*10^9*2*(1.65*10^-6)(4/0.0775^2)sin 135

E = 27972290.7321 N/C = 279.72290*10^5 N/C

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