Four infinite, non-conducting, thin sheets are arranged as shown below. Sheet C

Question

Four infinite, non-conducting, thin sheets are arranged as shown below. Sheet C has a uniform surface charge density of +5sigma The other three sheets have uniform surface charge densities of -2sigma, -4sigma, and +3sigma in some unknown order. In order to determine which charge densities belong to which plates, you make two electric field measurements, at the points labelled 1 and 2. Taking right to be the positive direction, the electric fields at these two points are: Place the surface charge densities on the plates in an arrangement that would result in the above measurements. Then, indicate the location at which the magnitude of the electric field is greatest. The magnitude of the electric field is greatest

Explanation / Answer

Since at point two direction of electric field is negative, i.e to the left, and also that plate C's electric field is rightward, so plate D should be positively charged, if we take plate D as +3 then rest of plates A and B are negatively charged and condition of electric field at 2 is satisfied.

Now electric field at 1 is also negative i.e. leftward. with similar logic, taking field due to C and D at 1, we can show that A is less negative and hence -2sigma;

Overall arrangement -> A is with -2sigma; B with -4 sigma and D with +3 sigma;

The magnitude of electric field will be greatest between B and C; since C and D are both positively charged so they will have a leftward field at this point while A and B(both negative) will also have a leftward field, hence total field will be highest here.

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