Podcast
Questions and Answers
A straight wire carries a current $I$. At a distance $R$ from the wire, the magnetic field $B$ is measured. If the current is doubled and the distance is also doubled, what happens to the magnetic field?
A straight wire carries a current $I$. At a distance $R$ from the wire, the magnetic field $B$ is measured. If the current is doubled and the distance is also doubled, what happens to the magnetic field?
- Is quadrupled
- Remains the same (correct)
- Is halved
- Is doubled
The magnetic field inside a solenoid is uniform and depends on the radius of the solenoid.
The magnetic field inside a solenoid is uniform and depends on the radius of the solenoid.
False (B)
A charged particle moves with a velocity $v$ in a magnetic field $B$. Under what condition will the magnetic force on the particle be zero?
A charged particle moves with a velocity $v$ in a magnetic field $B$. Under what condition will the magnetic force on the particle be zero?
when v is parallel to B
The torque on a current loop in a uniform magnetic field is given by $\tau = m \times B$, where $m$ is the ______.
The torque on a current loop in a uniform magnetic field is given by $\tau = m \times B$, where $m$ is the ______.
Match the current configurations with the appropriate formula for the magnetic field at a specific point:
Match the current configurations with the appropriate formula for the magnetic field at a specific point:
A wire carrying a current is placed in a magnetic field. According to Fleming's left-hand rule, which factors determine the direction of the force on the wire?
A wire carrying a current is placed in a magnetic field. According to Fleming's left-hand rule, which factors determine the direction of the force on the wire?
The work-energy theorem in magnetism states that the magnetic field does work on moving charges, changing their kinetic energy.
The work-energy theorem in magnetism states that the magnetic field does work on moving charges, changing their kinetic energy.
When a charged particle is projected into a magnetic field at an angle (other than 0 or 90 degrees), describe the resultant motion of the charged particle.
When a charged particle is projected into a magnetic field at an angle (other than 0 or 90 degrees), describe the resultant motion of the charged particle.
Flashcards
B-field of a Finite Wire
B-field of a Finite Wire
Magnetic field due to a finite wire at a distance R. θ₁ and θ₂ are angles from the point to the ends of the wire.
B-field of an Infinite Wire
B-field of an Infinite Wire
Magnetic field at a distance R from an infinitely long straight wire.
B-field at the center of a Circular Coil
B-field at the center of a Circular Coil
Magnetic field at the center of a circular loop of radius R.
B-field on the Axis of a Ring
B-field on the Axis of a Ring
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B-field Inside a Solenoid
B-field Inside a Solenoid
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Force on a Charged Particle
Force on a Charged Particle
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Torque on a Current Loop
Torque on a Current Loop
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Force on a Current-Carrying Wire
Force on a Current-Carrying Wire
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Study Notes
Magnetic Field Calculations
- Focus is primary on finding magnetic fields due to various current configurations.
- Covers straight wires (finite and infinite), circular coils, and solenoids
- Also covers the behavior of charged particles and current-carrying wires in magnetic fields.
- Excludes earth magnetism, magnetic materials (diamagnetic, ferromagnetic), and bar magnets, which will be covered later.
- Focus is on discussing and solving JEE Main questions related to the topics.
Key Formulas for Magnetic Field Due to Current-Carrying Wires
- Magnetic field (B) due to a finite wire: B = (μ₀I / 4πR) * (sin θ₂ - sin θ₁)
- R is the shortest distance to the wire.
- θ₁ and θ₂ are angles from the point to the ends of the wire.
- Magnetic field (B) due to an infinite wire: B = μ₀I / 2πR
- R is the shortest distance to the wire.
Key Formulas for Magnetic Field Due to Coils and Loops
- Magnetic field (B) at the center of a circular coil: B = μ₀I / 2R
- R is the radius of the loop.
- For a coil arc, B = (μ₀ / 4π) * (I / R) * θ
- θ must be in radians.
- Magnetic field (B) on the axis of a ring at distance x: B = (μ₀nIr²) / (2(r² + x²)^(3/2))
- n is the number of turns.
Solenoids
- Magnetic field (B) inside a solenoid: B = μ₀nI
- n is the number of turns per unit length.
Forces on Charged Particles in Magnetic Fields
- Force (F) on a charged particle: F = q(v × B)
- Used to find radius (r) if the particle moves in a circle: r = mv / qB
- If a charge is projected at an angle:
- Component of velocity parallel to B remains unaffected
- Component of velocity perpendicular to B causes circular motion.
- Time period (T) for a charged particle in a magnetic field: T = 2πm / qB
Magnetic Moment and Torque
- Magnetic moment (m): m = I * A, where A is the area vector.
- Torque (τ) on a loop in a uniform magnetic field: τ = m × B
Force on a Current-Carrying Wire in a Magnetic Field
- Force (F) on a wire: F = I(L × B)
- Use Fleming's left-hand rule to find direction.
Work-Energy Theorem in Magnetism
- Electric field work = change Kinetic Energy
- Relates speed changes to electrical work
Problem-Solving Strategies
- Converting complex arrangements into basic elements like infinite wires loops and arcs.
- Using symmetry to simplify magnetic field calculations.
- Recognizing standard configurations and applying formulas directly.
Important Considerations
- Electric Field & power with motion
- When calculating magnetic fields, choose the correct formula based on the geometry of the current source.
- Direction is crucial; use the right-hand rule or Fleming's left-hand rule.
- Remember formulas for magnetic moment and the torque on a current loop in a magnetic field
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Description
Calculations of magnetic fields due to current configurations including straight wires, circular coils, and solenoids. Includes formulas for calculating magnetic fields. Focus on JEE Main questions.
