Question

A wire in the form of a circular loop of one turn carrying a current produces a magnetic field B at the centre. If the same wire is looped into a coil of two turns and carries the same current, the new value of magnetic induction at the centre is

• A. 4B
• B. 2B
• C. 3B
• D. 5B

Answer 1

The Correct Option is A

A wire in the form of a circular loop of one turn carrying a current produces a magnetic field B at the centre. If the same wire is looped into a coil of two turns and carries the same current, the new value of magnetic induction at the centre is

The magnetic field at its center B = μ₀I/2πr

Thus the length of the wire L = 2πr

But the same wire is looped into a coil of radius r₂ of two turns

r₂ = r/2

The magnetic field at its center B = (μ₀I/2πr₂) x n = [μ₀I/2π(r/2)] x 2 = 4 x μ₀I/2πr =4B

\(B_{new} = n^2\) B = (2)\(^2\) B = 4B

Magnetic field, also called a vector field, represents the magnetic influence on moving electric charges, magnetic materials, and electric currents. The magnetic fields force moving electrically charged particles in a circular or helical path and the charged particles experience a force perpendicular to their own velocity and to the magnetic field. Magnetic field can be expressed as the area around a magnet wherein the effect of magnetism is felt.

• The symbol of the Magnetic Field can be denoted by B or H. It is denoted mathematically by quantities known as vectors which have direction and magnitude both. 
• Two different vectors help represent magnetic field: Magnetic flux density (or magnetic induction) and Magnetic field strength (or magnetic field intensity) each symbolized by B and H respectively.
• The unit of Magnetic Field is Telsa and its base unit is (Newton.Second)/Coulomb. 
• Magnetic field lines are known to not cross one another. In fact, magnetic lines form closed loops, beginning from the north pole and ending at the south pole. 
• The density of the field lines generally indicates the strength of the field.

Discover more from this chapter: Electromagnetic Induction

 

Answer 2

The Correct Answer is (A)

Real Life Applications

• The magnetic field at the center of a coil of wire is proportional to the number of turns in the coil is in the design of electrical devices that use magnetic fields. For example, the magnetic field produced by a coil of wire is used in loudspeakers, electric motors, and generators.In a loudspeaker, the coil of wire is attached to a diaphragm.
• In an electric motor, the coil of wire is attached to a rotor.
• In a generator, the coil of wire is attached to a rotating shaft.
• The fact that the magnetic field at the center of a coil of wire is proportional to the number of turns in the coil is a fundamental principle of electromagnetism. It is used in a wide variety of electrical devices, and it is essential for the operation of many modern technologies.

Question can also be asked as

• What is the magnetic field at the center of a coil with two turns?
• How does the magnetic field at the center of a coil change with the number of turns?
• What is the relationship between the magnetic field at the center of a coil and the current flowing through it?
• If the number of turns in a coil is doubled, what happens to the magnetic field at the center?

Answer 3

Properties of Magnetic Field Lines

Some of the important properties of Magnet Field Lines include:

• Magnetic field lines never cross each other.
• It follows the path with the least resistance between the opposing magnetic poles. A bar magnet's magnetic lines of force travel in closed loops from one pole to the other.
• Magnetic field lines will have the same length.
• The density of the field lines decreases as they pass from the higher permeability region to the lower permeability region.
• Lines travel from the south pole to the north pole within a material magnetic field, while in the air, they flow from the north pole to the south pole.
• The density of the magnetic field varies with distance from the pole. Their density reduces as one moves away from the pole.
• Because it has both magnitude and direction, the magnetic field is a vector quantity.

How is Magnetic Field Produced?

A magnetic field can be produced not just by a magnet, but also by a moving charge or electric currents. We are all aware that matter is made up of small bits known as atoms. An atom's nucleus is made up of protons and neutrons, with electrons orbiting around it.

The magnetic field is created by the spinning and circling of protons and neutrons or the nucleus of an atom. The magnetic field's direction is determined by the orbit and spin directions. The magnetic field is represented mathematically by the letter 'B.' Tesla is the