Askiitians Tutor Team
Last Activity: 5 Months ago
To find the potential difference between the top and bottom edges of a metallic strip subjected to a magnetic field, we can use the principles of electromagnetism, specifically the Hall effect. When a current-carrying conductor is placed in a magnetic field, a voltage is induced across the conductor, which is perpendicular to both the current and the magnetic field. Let's break this down step by step.
Understanding the Setup
We have a metallic strip with the following characteristics:
- Width: 'a'
- Cross-sectional area: 'S'
- Current: 'I'
- Concentration of electrons: 'n'
- Magnetic field: 'B', which is perpendicular to the strip
Applying the Hall Effect
When the current 'I' flows through the strip, it creates a magnetic force due to the magnetic field 'B'. This force acts on the charge carriers (electrons) moving through the strip. The force can be described by the equation:
F = q(v × B)
Where:
- F: Magnetic force on the charge carriers
- q: Charge of the electron (approximately -1.6 x 10-19 C)
- v: Drift velocity of the electrons
- B: Magnetic field strength
Calculating Drift Velocity
The drift velocity 'v' of the electrons can be calculated using the formula:
v = I / (n * A * q)
Where:
- A: Cross-sectional area 'S'
Finding the Hall Voltage
The Hall voltage (VH) induced across the width 'a' of the strip can be expressed as:
VH = B * I * (a / (n * q * S))
Here’s how we derive this:
- The magnetic force causes a separation of charge, leading to a potential difference across the width 'a'.
- The Hall voltage is directly proportional to the magnetic field strength 'B' and the current 'I'.
- It is inversely proportional to the product of the charge carrier concentration 'n', the charge 'q', and the cross-sectional area 'S'.
Final Expression for Potential Difference
Thus, the potential difference between the top and bottom edges of the metallic strip can be summarized as:
VH = \frac{B \cdot I \cdot a}{n \cdot q \cdot S}
This equation gives you a clear understanding of how the potential difference arises due to the interaction of the magnetic field with the current-carrying strip. The greater the magnetic field or current, the larger the potential difference, while a higher concentration of charge carriers or larger cross-sectional area reduces it.
