Q. 445.0( 1 Vote )

A circular coil of 200 turns has a radius of 10 cm and carries a current of 2.0 A.
(a) Find the magnitude of the magnetic field vector B at the center of the coil.

(b) At what distance from the center along the axis of the coil will the field B drop to half its value at the center?
(3√4 = 1.5874)

Answer :

Given:


Number of turns(n) = 200


Radius of circular coil(r) = 10 cm = 0.1 m


Current carried by the coil(i) = 2 A


Formula used:


(a) Magnetic field at the center of a circular coil of n turns(B) =


M=,


where


μ0 = magnetic permeability of vacuum = 4π x 10-7 T m A-1,


i = current carried by coil,


r = radius of coil


Hence, from the given information,


Magnetic field at the center of the given coil


= T = 2.51 x 10-3 T = 2.51 mT


(b) The magnetic field at a distance point in the coil is given by Bp,



The magnetic field at the center of the coil is


Given: the magnetic field at the center is 1/2 of the initial


The magnetic field at the center of the coil is


On equation the magnetic field at the center and the magnetic field at the any distant point from the coil, we get



On equating the above equation, we get


(r2 + x2)3 =4r6


We get


x2 + r2= 41/3r2


x2=0.58 r2


x2=0.5× 100=58


x=± 7.66 cm


Magnetic field will drop to half of its value at the center if the distance of that point from the center of the coil along the axis of coil is equal to 7.66 cm.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Magnetic field due to current carrying straight wireMagnetic field due to current carrying straight wireMagnetic field due to current carrying straight wire37 mins
Magnetic field due to current carrying circular loopMagnetic field due to current carrying circular loopMagnetic field due to current carrying circular loop36 mins
Interactive Quiz on Magnetic field due to straight wire & circular loopInteractive Quiz on Magnetic field due to straight wire & circular loopInteractive Quiz on Magnetic field due to straight wire & circular loop41 mins
Gain Confidence on Magnetic Effects of Current with QuestionsGain Confidence on Magnetic Effects of Current with QuestionsGain Confidence on Magnetic Effects of Current with Questions41 mins
Equation of electric and magnetic fieldEquation of electric and magnetic fieldEquation of electric and magnetic field52 mins
Magnetic force on moving charge particle in magnetic field | QuizMagnetic force on moving charge particle in magnetic field | QuizMagnetic force on moving charge particle in magnetic field | Quiz32 mins
Magnetic force on moving charge particle in magnetic fieldMagnetic force on moving charge particle in magnetic fieldMagnetic force on moving charge particle in magnetic field44 mins
Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)47 mins
Few Applications of Gauss's lawFew Applications of Gauss's lawFew Applications of Gauss's law54 mins
Electric field inside cavityElectric field inside cavityElectric field inside cavity37 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :