A single-turn coil of radius R produces a magnetic field B at its centre. If the same wire is wound into a coil of n turns (each of radius R/n) carrying the same current I, what will be the value of the new field at the centre?
\(n^2B\)
The magnetic field at the centre of a circular coil is \(B = \dfrac{\mu_0 N I}{2 r}\), where N is the number of turns and r is the radius.
For the single turn: \(B = \dfrac{\mu_0 I}{2R}\).
When the same wire is rewound into n turns, each turn has radius \(r = \dfrac{R}{n}\) and N = n.
New field \(B' = \dfrac{\mu_0 (n) I}{2 (R/n)} = \dfrac{\mu_0 n^2 I}{2R}\).
Comparing, \(B' = n^2 \cdot \dfrac{\mu_0 I}{2R} = n^2 B\).
Hence, the new field at the centre is \(n^2 B\).
Similar Questions
The direction of the magnetic field at the centre of a current-carrying circular loop is determined by which of the following?
A device uses the principle of magnetic fields around a current-carrying conductor to convert electrical energy to mechanical energy. Which device operates on this principle?
What happens when a conductor moves through a magnetic field?
What does a higher degree of closeness of magnetic field lines indicate?
If the current in a conductor is doubled while it remains perpendicular to the same magnetic field, how does the force on the conductor change?
Which arrangement will result in the greatest induced current in a wire loop?
In an experiment, a metal rod moves northward across a horizontal magnetic field directed east. According to Fleming's Right Hand Rule, what is the direction of the induced current in the rod?
Which statement best describes the application of the Right Hand Thumb Rule to a straight current-carrying conductor?
Two identical coils are placed near each other. If the current in the first coil is switched off suddenly, what will happen in the second coil?
What happens to the magnetic field around a straight current-carrying conductor if the direction of the current is reversed?
Important Questions from Magnetism
What is the direction of magnetic field lines outside a magnet?
Which of the following statement is correct?
।. Magnetic field has both magnitude and direction.
II. The magnetic field inside a current-carrying straight long solenoid is the same at all points.
The magnetic effect of electric current was discovered by _____.
The important property of magnet which was exploited by navigators and travelers from the ancient times is:
The magnet used to lift and transport heavy loads like big metals, steel girders and scrap iron objects for loading and unloading purposes is known as____.
