Q. 174.2( 11 Votes )

A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound.

If the current in the wire is 11 A, what is the magnetic field

(a) outside the toroid,

(b) inside the core of the toroid, and

(c) in the empty space surrounded by the toroid.

Answer :

The Toroid is same as a solenoid but is bound in a circular region as compared to straight cylindrical region in a solenoid the length of a toroid is given by L = 2πR, (Perimeter of a Circle)


where R is mean radius of cross section of toroid


= 25.5 cm = 0.255 m


here Total number of turns of toroid N = 3500,


no. of turns per unit length n = N/L = = 2475.74/m


the current flowing in Toroid I = 11 A


The toroid has been shown in the following figure



(a) Since Toroid is same as a solenoid so magnetic field outside the toroid = 0 T same as in case of solenoid.


Explanation: if we apply Ampere Circuital Law to find magnetic field B at small element dl due to a current carrying conductor with current I flowing through it and is permittivity of free space, outside the solenoid or toroid, where there is no conductor/wire/current carrying loop, the current I = 0 so we get So Integrating over length l we get Bl = 0 so magnetic field B = 0 i.e. at all places where there is no current carrying loop magnetic field B = 0


(b) The magnetic field in the inner core of toroid is given by


B = 𝜇onI


Where n is no. of turns per unit length,


I is the current flowing in Toroid,


𝜇o is the permittivity of free space = TmA-1


So putting all values, B = = T


i.e. Magnetic field inside core is 0.03 T.


(c) Again it’s the same case as of exterior of a solenoid as explained above so magnetic field is Zero, here also in the empty space between the toroid.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz on Magnetic field due to straight wire & circular loop41 mins
Magnetic force on moving charge particle in magnetic field44 mins
Cyclotron37 mins
Magnetic field due to current carrying straight wire37 mins
Magnetic field due to current carrying circular loop36 mins
Magnetic force on moving charge particle in magnetic field | Quiz32 mins
Lorentz force & its applications33 mins
Electric Charges and Fields - 0556 mins
Electric Charges and Fields - 0352 mins
Electric Charges and Fields - 0155 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
view all courses
RELATED QUESTIONS :