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# Dimensional analysis and electric fields

last edited by 3 years, 2 months ago

8.1.P5

The functional dependence of the electric field from some highly symmetric shapes can be determined rather straightforwardly from dimensional analysis. Given that the electric field is defined by the equation F = qE and the force on a point charge q from a charge Q a distance r away is F = kCqQ/r2

A. Find the dimensionality of the Coulomb constant kC and the electric field, E, in terms of the basic dimensions, M, L, T, and Q. Show your work.

B. For a long uniform line of charge, we know neither the total charge on the line nor its length, only the charge per unit length, λ, with units of Coulomb/meter. Assuming that the dependence of the E-field produced by that line as a function of the (perpendicular) distance d from the line will look something like E = αkCλ/dn,where α is a dimensionless constant. Use dimensional analysis to find the value of n. If you can find it, show your work below. If you can't, explain why not.

C. For a large flat uniform sheet of charge, we know neither the total charge on the sheet nor its area, only the charge per unit area, σ, with units of Coulomb/meter2. Assuming that the dependence of the E-field produced by that line as a function of the (perpendicular) distance from the sheet will look something like E = αkCσ/dn,where α is a dimensionless constant. Use dimensional analysis to find the value of n. If you can find it, show your work below. If you can't, explain why not.

Joe Redish 3/4/16