Question

magnetic effect of current Concept ,Application , real time examples for jee mains

Answer 1

The explanation above covers the concept, application (principles/laws), and real-time examples of the magnetic effect of current relevant for JEE Mains.

Answer 2

Explanation of the Solution

The magnetic effect of current refers to the phenomenon where an electric current flowing through a conductor produces a magnetic field around it. This fundamental concept was discovered by Hans Christian Oersted.

Concept

When charge flows (current), it creates a magnetic field in the surrounding space. The strength and direction of this magnetic field depend on the magnitude and direction of the current, and the geometry of the conductor.

Application (Principles & Laws)

1. Direction of Magnetic Field:

   • Right-Hand Thumb Rule: For a straight current-carrying conductor, if you point your right thumb in the direction of the current, your curled fingers indicate the direction of the magnetic field lines around the conductor. For a current loop, if your fingers curl in the direction of the current, your thumb points in the direction of the magnetic field inside the loop (along its axis).

2. Magnetic Field (B) due to Current Configurations:

   • Biot-Savart Law: Provides the general formula for the magnetic field $\vec{dB}$ produced by a current element $I d\vec{l}$: $\vec{dB} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \vec{r}}{r^3}$ where $\mu_0$ is the permeability of free space.
   • Ampere's Circuital Law: Useful for symmetric current distributions: $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$
   • Infinite Straight Wire: $B = \frac{\mu_0 I}{2\pi r}$
   • Circular Loop (at center): $B = \frac{\mu_0 N I}{2 R}$ (for N turns)
   • Solenoid (inside): $B = \mu_0 n I$ (where $n$ is turns per unit length)

3. Force on a Current-Carrying Conductor in a Magnetic Field:

   • A conductor of length $L$ carrying current $I$ placed in a uniform magnetic field $\vec{B}$ experiences a force $\vec{F}$: $\vec{F} = I (\vec{L} \times \vec{B})$ Magnitude: $F = I L B \sin\theta$, where $\theta$ is the angle between $\vec{L}$ and $\vec{B}$.
   • Fleming's Left-Hand Rule: Used to determine the direction of force (Thumb: Force, Forefinger: Field, Middle finger: Current).

4. Force Between Two Parallel Current-Carrying Wires:

   • Two parallel wires carrying currents $I_1$ and $I_2$ separated by distance $d$ exert a force on each other. The force per unit length is: $\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}$
   • Direction: Attractive if currents are in the same direction, repulsive if in opposite directions.

5. Torque on a Current Loop in a Magnetic Field:

   • A current loop with magnetic dipole moment $\vec{M} = NI\vec{A}$ (where $N$ is turns, $I$ is current, $\vec{A}$ is area vector) in a magnetic field $\vec{B}$ experiences a torque $\vec{\tau}$: $\vec{\tau} = \vec{M} \times \vec{B}$ Magnitude: $\tau = NIAB \sin\theta$, where $\theta$ is the angle between $\vec{M}$ and $\vec{B}$.

Real-Time Examples for JEE Mains

1. Electromagnets: Temporary magnets created by passing current through a coil wound around a ferromagnetic core. Used in:

   • Electric Bells: Current through a coil attracts an armature, striking a gong.
   • Cranes: Lift heavy magnetic materials.
   • Relays: Electrically operated switches.
   • Circuit Breakers: Interrupt current flow in case of overload.

2. Electric Motors: Devices that convert electrical energy into mechanical energy. They work on the principle that a current-carrying coil placed in a magnetic field experiences a torque, causing it to rotate.

3. Galvanometers: Instruments used to detect and measure small electric currents. They utilize the torque experienced by a current-carrying coil in a magnetic field, causing a pointer deflection proportional to the current.

4. Loudspeakers: Convert electrical audio signals into sound waves. A coil attached to a cone carries the audio current, interacting with a permanent magnet to produce vibrations that generate sound.

5. Magnetic Resonance Imaging (MRI): A medical imaging technique that uses strong magnetic fields and radio waves to create detailed images of organs and tissues inside the body. It relies on the magnetic properties of atomic nuclei.

6. Magnetic Levitation (Maglev Trains): Use powerful electromagnets to lift, propel, and guide trains above a guideway, eliminating friction and enabling very high speeds.