Ranking Tasks an arrangement of four charges. Each charge has magnitude and sign

Question

Ranking Tasks an arrangement of four charges. Each charge has magnitude and sign as given in the images 20 +20 +20 .20 +20 Rank the magnitude of the electrie field at the location marked with an x. Greatest 1 3 The figures below show cross-sections of spherical or cubical Gaussian surfaces that intersect solid charged spheres. The total charge+Q is the same for the conducting sphere on the left and the uniformly charged insulating sphere on the right. The radii of surfaces A, C, and D are half that of the conducting and insulating spheres. 2· +0 +0 Conductori Insulator Rank the total electric flux through the surfaces labeled A-E: Greatest 1 -2- 4-5 Least

Explanation / Answer

1. Given 6 figures with charge distribution as shown

consider, y axis to point upwards and x axis to point to the right

Figure A.

all the charges are of same charge and magnitude, hence from symmetry

electric field E = 0

Figure B.

the top and bottom charges are symmetrically places

the left and right charge add up to give E = 2kQ/a^2

let kQ/a^2 = Eo

E = 2Eo ( in +x direction)

Figure C.

charge distribution is symmetrical about the center point

so E = 0

Figure D. form previous parts

E = 2Eo i - 2Eo j

|E| = 2*sqrt(2)*Eo

Figure E. top and bottom charges cancel out each others field

E = 2Eo

Figure F. all charges are symmetrically placed wrt center, so E = 0

hence

ranking the electric field we get

Ed > Ee = Eb > Ea = Ec = Ef

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