Magnetics-03-SUBJECTIVE SOLVED

SUBJECTIVE SOLVED EXAMPLES 1. A circular loop of radius R is bent along a diameter and given a shape as shown in figure. One of the semi-circles (KNM) lies in y the x-z plane and the other one (KLM) in the y-z plane with their centres at origin. Current I is flowing through each of the semi- x circles as shown in figure. z → A particle of charge q is released at the origin with a velocity  V iˆ . Find the instantaneous force → on the particle. Assuem that space is gravity free. Solution :Magnetic field at the centre of a circular wire of radius R carrying a current I is given by B  0I 2R In this problem, currents are flowing in two semi-circles, KLM in the y-z plane and KNM in the x- z plane. The centres of these semi-circles coincide with the origin of the Cartesian system of axes.  → 1  0I  ˆ BKLM   (i) 2  2R  → 1  0I  ˆ BKNM   (j) 2  2R  The total magnetic field at the origin is B  0I (ˆi  ˆj) 0 4R It is given that a particle of charge q is released at the origin with a velocity V = - instantaneous force acting on this particle is given by V0ˆi . The → → f  q[V B]  q(V ˆi)  0I (ˆi  ˆj) 0  4R    q V00I  ˆ ˆ ˆ  4R [(i) (i  j)   q V00I (kˆ) . 4R 2. A coil of radius R carries current I. Another concentric coil of radius (r <

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