Given that q and Q represent charges (dimensionality Q), lambda a charge per uni

Question

Given that q and Q represent charges (dimensionality Q), lambda a charge per unit length (dimensionality Q/L), and sigma a charge per unit area (dimensionality Q/L^2), consider the following expressions: k_C Q/x^2 2k_C lambda/x^2 2 pi k_C q sigma/x^2 k_C qQ/x^2 2 k_C lambda/x 2 pi k_C sigma k_c qQ/x 2k_C q lambda/x^2 2 pi k_C q sigma Using dimensional analysis, select which of these could give a good representation of the following physical quantities (or select N if none of these could work). The electric field at a distance x from a point charge Q. The electric potential energy of a test charge q a distance x from a point charge Q. The electric force on a test charge q a distance x from a line charge, density lambda. The electric field at a distance x from a plane of charge, density sigma. The electric force on a test charge, q, a distance x from a plane of charge, sigma. Explain your reasonings.

Explanation / Answer

1) the electric fiedl ata distance x from a point charge Q i s E = kq/x^2

   so the appropriate option is------ A

2) elelctric potential energy is U = kq1*q2/r , so the option G is correct dimensionally -------G

3)force on a test charge ata distance x from a line of charge density Lambds is

   F = kq*Lambda*l/x^2   ; no option is there so answer is N

4) electric field at a distnce x from plane of charge , density sigma

   E = k*sigma*l^2/x^2 --------- which is suitable dimensionally is option -- F

5)

electric force on a test charge q at a distance x from aplane of charge sigma

   F = kq*sigma*l^2/(x^2)

dimensionally it is correct with option I -- 2pi*k *q*sigma

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