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 \(\overrightarrow{J} = \sigma \overrightarrow{E}\)

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Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

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Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

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If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

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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

1.Four independent waves are expressed as \[ (i)\; y_1=A_1\sin\omega t, \] \[ (ii)\; y_2=A_2\sin 2\omega t, \] \[ (iii)\; y_3=A_3\cos\omega t, \] \[ (iv)\; y_4=A_4\sin\left(\omega t+\frac{\pi}{3}\right) \] The interference between two of these waves is possible in

2.Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

3. Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

4. Write any two features of nuclear forces.

6. If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Four independent waves are expressed as \[ (i)\; y_1=A_1\sin\omega t, \] \[ (ii)\; y_2=A_2\sin 2\omega t, \] \[ (iii)\; y_3=A_3\cos\omega t, \] \[ (iv)\; y_4=A_4\sin\left(\omega t+\frac{\pi}{3}\right) \] The interference between two of these waves is possible in

2.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

3.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

4.
Write any two features of nuclear forces.

6.
If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.