Drift Velocity

Drift Velocity and Mobility

We are asked to identify the term that defines the magnitude of the drift velocity per unit electric field.

Step 1: Define Drift Velocity

Drift velocity ( ) is the average velocity that charge carriers (e.g., electrons in a metal) attain due to an electric field. It's the net velocity of the charge carriers in a particular direction.

Step 2: Define Mobility

Mobility ( ) is defined as the drift velocity per unit electric field:

Where:

• is the mobility.
• is the magnitude of the drift velocity.
• is the magnitude of the electric field.

Step 3: Why Conductivity is Incorrect

Conductivity ( ) is a measure of a material's ability to conduct electric current. It is related to the drift velocity and mobility, but it is not the *definition* of drift velocity per unit electric field. Conductivity is given by:

Where:

• is the conductivity.
• is the number density of charge carriers.
• is the charge of the charge carrier.
• is the mobility.

Conductivity depends on both mobility AND the density and charge of the carriers.

Conclusion

The magnitude of the drift velocity per unit electric field is defined as Mobility.

Step 1: The bus is moving with constant velocity, and the boy inside the bus throws the ball vertically. From the reference frame of the bus, the ball will appear to move vertically upward.
However, from an external observer's frame (e.g., outside the bus), the ball will have both a horizontal and vertical velocity.
Since the ball's horizontal velocity matches that of the bus, it will fall back in the hands of the boy.

Step 1: The Bohr model is applicable to hydrogen-like atoms, where there is a single electron in orbit around the nucleus. For other atoms with multiple electrons, the Bohr model fails to explain their behavior accurately.
Step 2: In the case of a doubly ionized helium atom, the atom has no electrons, making the Bohr model invalid for such systems. Therefore, the Bohr model does not work for the doubly ionized helium atom.

Step 1: At resonance in an LCR circuit, the impedance is purely resistive, meaning the total reactance (inductive and capacitive) is zero.
Step 2: The power factor in an LCR circuit is given by: At resonance, , hence: Thus, the power factor at resonance is 1.

We are given the equation for the travelling wave as: where is the displacement, is the amplitude, is the angular velocity, is the linear velocity, is the position, and is time.
We need to find the dimensions of .
Step 1: The general dimension formula for angular velocity is: Step 2: The dimension of time is simply: Step 3: Thus, the product has the dimension: Therefore, the dimension of is .

Step 1: The terminal potential difference is related to the emf , the internal resistance , and the external resistance by: where is the current.
Step 2: The current is: Substitute this into the equation for : Step 3: Given , , and , we can solve for : Step 4: Solving for : Thus, the internal resistance of the cell is .

Step 1: The process described in the question is the fusion of hydrogen nuclei to form a helium nucleus, which is a typical example of nuclear fusion.
Step 2: In nuclear fusion, multiple light nuclei (in this case, hydrogen atoms) combine to form a heavier nucleus (helium), releasing a large amount of energy. The energy released here is 26.7 MeV, which is characteristic of fusion reactions.
Step 3: Therefore, the process described is a fusion reaction.

Step 1: The impulse imparted to the gun by firing one bullet is equal to the change in momentum of the bullet.
The momentum of one bullet is: The maximum force on the gun is , and the time taken to impart this force for each bullet is: Thus, the maximum number of bullets fired per second is:

Step 1: The energy equivalent of mass is given by Einstein's equation:
where:
- ,
- .
Step 2: Substitute the values into the equation:
Thus, the energy equivalent of 1 g of substance is .