What is vector form of ohms law ?

Asked by  | 12th Feb, 2010, 08:08: PM

Expert Answer:

Dear student,

Simplest ohm's law is

v = I R

where is the voltage drop across a resistor of resistance when a current flows through it. Let us generalize this law so that it is expressed in terms of and , rather than and . Consider a length of a conductor of uniform cross-sectional area with a current flowing down it. In general, we expect the electrical resistance of the conductor to be proportional to its length, and inversely proportional to its area (i.e., it is harder to push an electrical current down a long rather than a short wire, and it is easier to push a current down a wide rather than a narrow conducting channel.) Thus, we can write

R = ρ l/A

The constant ρ  is called the resistivity, and is measured in units of ohm-meters. Ohm's law becomes

V = ρ l/A I

However, (supposing that the conductor is aligned along the -axis) and , so the above equation reduces to

Ez = ρ jz

There is nothing special about the -axis (in an isotropic conducting medium), so the previous formula immediately generalizes to

E = ρj

Hope this helps.


Answered by  | 13th Feb, 2010, 10:44: AM

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