Obtain the equation J = sigma. E of Ohm's law on the basis of drift velocity.

Step 1: Ohm's law and its parameters

1. Ohm’s law states that voltage across a resistance is directly proportional to the current flowing through it when temperature and other physical conditions remain constant with time.
2. Ohm's law is denoted by the formula V = IR, where, I is the current flowing through resistance, R is the constant of proportionality or resistance and V is the voltage.
3. \(\overrightarrow{J} = \sigma \overrightarrow{E}\) is the vector form of Ohm's law, in which, J refers to the current density, which is defined as \(J = {Current\ flow (I)\over cross\ sectional\ area\ (A)}\)E refers to the electric field and \(\sigma\) is the conductance of the resistance.

Step 2: Resistance and conductivity

The resistance, \(R = \rho {L \over A}\)where \(\rho\)  is the resistivity, L and A are the length and area of the conductor.

Conductivity is the reciprocal of resistivity, i.e, \(\sigma = {1 \over \rho}\).

Step 3: Finding the expression \(\overrightarrow{J} = \sigma \overrightarrow{E}\)

As J = \({ I \over A}\)

or J = \({ V \over RA}\) (As from Ohm’s Law V = IR)

or J = \({ V \over A (\rho {L \over A})} = {V \over \rho L}\) (since resistance \(R = \rho {L \over A}\))

or J = \({EL \over L \times \rho} = {E \over \rho} (since\ V = EL)\)

or J = \(E \sigma\ (\sigma = {1 \over \rho})\)

So, as a vector form \(\overrightarrow{J} = \sigma \overrightarrow{E}\)

Read More: Ohm’s Law and its Limitations

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Related Questions

1. What is the necessary condition for a conductor to obey Ohm's Law?
2. Why is the curve representing Ohm's law linear?
3. State Ohms law. How can it be verified experimentally?
4. How do you find the resistance to Ohm's law?
5. What are the 3 forms of Ohm's law
6. What are the limitations of Ohm's Law?
7. What are the applications of ohm's law used in daily life?
8. State Ohms Law. Express It Mathematically. Define Si Unit Of Resistance.
9. Is resistance constant in Ohm's law?
10. Draw a circuit diagram to verify ohm’s law.

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