Q17 of 31 Page 170

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.

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 =

More from this chapter

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15

A magnetic field of 100 G (1 G = 10–4 T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10–3 m2. The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m–1. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

 16

For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by,


(a) Show that this reduces to the familiar result for field at the centre of the coil.


(b) Consider two parallel co-axial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by,


, approximately.


[Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]

 18

Answer the following questions:

A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?

 18

Answer the following questions:

A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?