Magnetic Force on a Current-Carrying Conductor, as detailed in Chapter Four of the NCERT textbook "MOVING CHARGES AND MAGNETISM" for Class 12 Physics (New Edition), is crucial for students preparing for competitive exams like JEE, and NEET. This topic, covered comprehensively in NCERT and RBSE curricula, explores how electric currents interact with magnetic fields to produce a force. Understanding this phenomenon is crucial for academic success and grasping electromagnetism's role in modern engineering.
Magnetic Force on a Current-Carrying Conductor
Fundamental Principle
When a conductor carrying an electric current is placed in a magnetic field, it experiences a force and that is known as the Lorentz force.
Lorentz Force
The Lorentz force law states that the force (F) experienced by a charge (q) moving with velocity (v) in a magnetic field (B) is given by
`\vec F = q ( \vec v \times \vec B )`
For a current-carrying conductor, the force can be extended to account for the entire conductor rather than individual charges.
Magnetic Force on a Conductor
Consider a rod with uniform cross-sectional area A and length `l`, containing mobile charge carriers (electrons) with number density `n`. The total number of carriers is `n l A`. For a steady current I, each charge carrier has an average first velocity `v_d`. In the presence of an external magnetic field B, the force is
`\vec F = q ( \vec v_d \times \vec B )`
Derivation of Magnetic Force
`\vec F = q ( \vec v_d \times \vec B )`
`\vec F = N e ( \vec v_d \times \vec B )`
`\vec F = n V e ( \vec v_d \times \vec B )`
`\vec F = n A l e ( \vec v_d \times \vec B )`
`\vec F = n A l e ( \vec v_d \times \vec B )`
`\vec F = n A l e \vec v_d \vec B sin\theta `
`\vec F = n A e \vec v_d l \vec B sin\theta `
|`\vec F |= n A e v_d l B sin\theta `
|`\vec F| = I l B sin\theta `
In vector form
`\vec F = I ( \vec l \times \vec B )`
Where,
`N =` Number of electrons,
`n` = Number density of mobile charge carriers,
`l =` Length of rod,
`A =` Cross-sectional area of rod,
`v_d =` Drift velocity of charge carriers.
`B =` Intensity of external magnetic field
☆ If `\theta = 0^\circ`, the current carrying conductor is placed in the direction of the magnetic field, then
`\vec F = I ( \vec l \times \vec B )`
` F = I l B sin\theta `
` F = I l B sin 0^\circ `
` F = I l B (0) `
` F = 0 `
Due to F = 0, the conductor is stable.
☆ If `\theta = 90^\circ`, the current carrying conductor is placed perpendicular to the magnetic field, then
`\vec F = I ( \vec l \times \vec B )`
` F = I l B sin\theta `
` F = I l B sin 90^\circ `
` F = I l B (1) `
` F = I l B`
` F_{max} = I l B`
This is the maximum force on the current-carrying conductor in a uniform magnetic field.
Conclusion
Direction on Current
The direction of `\vec l` is in the direction of the current of the conductor.
Direction of the Force
The direction of force on the current carrying conductor is perpendicular to the plane formed by `l` and `\vec B` according to Right Hand Screw Rule.
Point your thumb in the direction of the current `(l)`, your finger in the direction of the magnetic field (B), and your palm will face the direction of the force (F).
Related Questions
☆ What is the formula for magnetic force?
☆ What is the Lorentz force?
☆ Express the magnetic force on a rod carrying a current I in vector form.
☆ Using the right-hand rule, how do you determine the direction of the magnetic force of a current-carrying conductor?
☆ What is the magnetic force on a current-carrying conductor?
☆ What is the magnetic force?
☆ What is the magnetic force on a current-carrying conductor in vector form?
☆ What is the maximum force on a current-carrying conductor?
☆ What is the number density?
☆ How is the total number of mobile charge carriers in a rod determined?
☆ Define current density.
No comments:
Post a Comment