Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Magnetic field due to a circular loop: The magnetic field lines are concentric circles at every point of the current-carrying circular loop. At the center of the loop, these lines appear as straight lines.
The magnetic field produced by a circular coil is directly proportional to the current passing through it () and inversely proportional to the radius of the loop ().
If there is a coil having turns, the field produced is times as large as that produced by a single turn, because the current in each circular turn has the same direction and the fields due to each turn add up.
Solenoid: A coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder is called a solenoid.
The magnetic field pattern of a solenoid is similar to that of a bar magnet. One end of the solenoid behaves as a magnetic North pole, while the other behaves as a South pole.
Magnetic field inside a solenoid: The field lines inside the solenoid are in the form of parallel straight lines. This indicates that the magnetic field is uniform at all points inside the solenoid.
Electromagnet: A strong magnetic field produced inside a solenoid can be used to magnetize a piece of magnetic material, like soft iron, when placed inside the coil. The magnet so formed is called an electromagnet.
📐Formulae
💡Examples
Problem 1:
A circular coil of turns has a radius of and carries a current of . If the number of turns is doubled to and the current remains the same, how does the magnetic field at the center change?
Solution:
The magnetic field at the center of a circular coil is directly proportional to the number of turns . Since , if increases from to (doubled), the magnetic field will also double.
Explanation:
In a coil with turns, the magnetic field produced by each turn adds up because the current flows in the same direction in all turns. Thus, .
Problem 2:
Identify the nature of the magnetic field inside a long current-carrying solenoid. If a soft iron core is inserted, what happens to the field strength?
Solution:
The magnetic field inside a long solenoid consists of parallel straight lines, indicating a uniform magnetic field. Inserting a soft iron core significantly increases the magnetic field strength, forming an electromagnet.
Explanation:
Soft iron has high permeability, which concentrates the magnetic field lines, thereby increasing the total magnetic induction inside the solenoid.