The force on a charge in an electric field is

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Quantities, units and the practice of measurement · Quantities, units and the practice of measurement

Measurement and Method, Ch What dimensions decide before you measure anything

Problem

The force on a charge qq in an electric field EE is F=qEF = qE, with electric current carrying the base dimension I\mathsf{I} so that charge has dimension dim⁡(q)=IT\dim(q) = \mathsf{I}\mathsf{T}. ((a)) Write dim⁡(E)\dim(E) in terms of the base dimensions. ((b)) Between two parallel plates a distance dd apart with a potential difference VV across them, the field is quoted as E=V/dE = V/d, where VV is potential energy per unit charge. Check whether this is dimensionally homogeneous, using your result from (a).

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