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What is the relationship between current...

What is the relationship between current density and drift velocity?

A

`J = n e v_(d)`

B

`J= e v_(d//n)`

C

`J = n //e v_(d)`

D

`J= n v_(d)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the relationship between current density (j) and drift velocity (vd), we can start from the fundamental definitions and equations in current electricity. ### Step-by-Step Solution: 1. **Understanding Current Density (j)**: - Current density (j) is defined as the current (I) flowing per unit area (A) through a conductor. Mathematically, it is expressed as: \[ j = \frac{I}{A} \] 2. **Defining Drift Velocity (vd)**: - Drift velocity (vd) is the average velocity that a charge carrier, such as an electron, attains due to an electric field. It is a measure of how quickly the charge carriers move through the conductor. 3. **Relating Current, Charge, and Drift Velocity**: - The current (I) can also be expressed in terms of charge (Q) and time (t): \[ I = \frac{Q}{t} \] - For a conductor with n free charge carriers (electrons) per unit volume, the total charge (Q) that passes through a cross-sectional area in time t can be given by: \[ Q = n \cdot A \cdot vd \cdot t \] - Here, \(n\) is the number of charge carriers per unit volume, \(A\) is the cross-sectional area, and \(vd\) is the drift velocity. 4. **Substituting into the Current Equation**: - Substituting this expression for Q into the equation for current (I): \[ I = \frac{n \cdot A \cdot vd \cdot t}{t} = n \cdot A \cdot vd \] 5. **Substituting into Current Density Equation**: - Now substituting this expression for I back into the equation for current density (j): \[ j = \frac{I}{A} = \frac{n \cdot A \cdot vd}{A} = n \cdot vd \] 6. **Final Relationship**: - Therefore, we arrive at the relationship between current density and drift velocity: \[ j = n \cdot e \cdot vd \] - Here, \(e\) is the charge of an electron. Thus, the relationship can also be expressed as: \[ j = n \cdot e \cdot vd \] ### Conclusion: The correct relationship between current density (j) and drift velocity (vd) is given by: \[ j = n \cdot e \cdot vd \]

To find the relationship between current density (j) and drift velocity (vd), we can start from the fundamental definitions and equations in current electricity. ### Step-by-Step Solution: 1. **Understanding Current Density (j)**: - Current density (j) is defined as the current (I) flowing per unit area (A) through a conductor. Mathematically, it is expressed as: \[ j = \frac{I}{A} ...
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