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

Step 1: Ohm's law and its parameters

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.
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.
$\overrightarrow{J} = \sigma \overrightarrow{E}$ 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 $\overrightarrow{J} = \sigma \overrightarrow{E}$

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

Step 1: Ohm's law and its parameters

Step 2: Resistance and conductivity

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

Related Questions

CBSE CLASS XII Related Questions

2.
Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

4.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

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

Step 1: Ohm's law and its parameters

Step 2: Resistance and conductivity

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

Related Questions

CBSE CLASS XII Related Questions

2.Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

4.Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

2.
Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

4.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?