ADDITIONAL EXERCISES . Two concentric circular coils X and Y of radii cm and cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has turns and carries a current of A; coil Y has turns and carries a current of A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west.
Give the magnitude and direction of the net magnetic field due to the coils at their centre. . A magnetic field of G ( G = – T) is required which is uniform in a region of linear dimension about cm and area of cross-section about – m . The maximum current-carrying capacity of a given coil of wire is A and the number of turns per unit length that can be wound round a core is at most turns m – .
Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic. . 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, ( / IR N B x µ (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, . NI B µ , approximately. [Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils .] .
A toroid has a core (non-ferromagnetic) of inner radius cm and outer radius cm, around which turns of a wire are wound. If the current in the wire is 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 following questions: (a) 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