Magnetic Effect Of Current Formula

The magnetic effect of current is also known as electromagnetism. Danish scientist Hans Christian Ørsted first discovered the phenomenon. A magnetic field is the region around a magnet or a current-carrying conductor in which another magnet or magnetic material can experience a magnetic force.

Some important points

A magnetic field is a vector quantity that has both direction and magnitude.
Magnetic field lines are closed curves.
It is taken by convention that the field lines emerge from the north pole and merge at the south pole.
The closeness of the field lines shows the relative strength of the magnetic field.
With the increase of current through the wire, the magnitude of the magnetic field produced by an electric current increases.
No two field lines are found to cross each other.

Magnetic Field Due To A Current-Carrying Conductor

The magnetic field produced by a straight current-carrying conductor is in the form of concentric circles. The Right-Hand Thumb Rule can determine the direction of the magnetic field.

Right-Hand Thumb Rule

If the thumb of the right hand points in the direction of current (I), then the curled fingers show the direction of the magnetic field (B).

Magnetic Field due to Current through a Straight Wire

formula

where

B = magnetic field (T)
μ₀ = 4π × 10⁻⁷ T·m/A
I = current (A)
r = perpendicular distance from wire (m)

Magnetic Field due to Current through a Circular Loop

formula

where

N = number of turns
R = radius of loop

Magnetic Field due to Current in a Solenoid

A solenoid is a coil of many circular turns in the shape of a cylinder. When current passes through it, it generates a magnetic field similar to that of a bar magnet.

B = μ₀nI

where

B = Magnetic Field (Tesla ‘T’)

μ₀ = Permeability of free space (4π × 10⁻⁷ T·m/A)

I = Current (Amperes ‘A’)

n = N/L = number of turns per unit length

how field lines look for a solenoid

Factors Affecting the Strength of the Magnetic Field

Number of turns (N/n): More turns produce a stronger field.
Distance (r): An increase in distance reduces the strength of the field.
Current (I): More current increases the strength of the field.
Material: Strength also depends on the type of material used.

Note: In solenoids, inserting a soft iron core greatly increases magnetic field strength.

Applications

Electric Motors: They convert electrical energy into mechanical energy. It utilises the force exerted on a current-carrying wire within a magnetic field to produce rotational motion.
Generators: They use the magnetic effect to convert mechanical energy into electrical energy. They induce a current in a conductor by moving it through a magnetic field, a process known as electromagnetic induction.
Transformers: Transformers utilise electromagnetic induction to transfer electrical energy from one circuit to another, often changing the voltage level.
Magnetic Resonance Imaging (MRI): MRI machines use strong magnetic fields and radio waves to create detailed images of the inside of the human body.
Loudspeakers: Loudspeakers use electromagnets to convert electrical signals into sound waves. The varying current in the electromagnet creates a changing magnetic field that vibrates a diaphragm, producing sound.

Summing Up

The magnetic effect of electric current shows that a current-carrying conductor produces a magnetic field in the region. The direction of the magnetic field can be identified using the Right-Hand Thumb Rule. The strength of a magnetic field depends on factors like current, distance, and number of turns. These concepts are used in devices like motors, generators, loudspeakers, etc. The principle of the magnetic effect of electric current links electricity and magnetism.

Frequently Asked Questions

Q1. Why do two magnetic field lines not intersect?

If two magnetic fields intersect, which means the field has two directions at the same point, this is not possible. Hence, it proves that magnetic field lines do not intersect.

Q2. State Right-Hand Thumb Rule.

If the thumb of the right hand points in the direction of current (I), then the curled fingers show the direction of the magnetic field (B).

Q3. What is a solenoid?

A solenoid is a long coil of wire wound in circular turns in the shape of a cylinder and behaves like a bar magnet.