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Obtain an expression for the torque on a current carrying loop placed in a uniform magnetic field. Describe the construction and working of a moving coil galvanometer. |
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Answer» Solution :Torque acting on a coil carrying a CURRENT kept in a uniform magnetic field : Let a reactangular current loop ABCD of length l =AB =CD and width b=AD=BC carrying a current ''I'' be suspended in magnetic field of flux density B. The normal ON drawn to the plane of the coil makes an angle `'theta'` with the magnetic field B.  Force on arm `AD= i barbxxbarB` acting upwards along the axis of suspension Force on arm `BC=i barbxxbarB` acting downwards along the axis of suspension Hence these two forces cancel.  Force on arm AB= ilB acting perpendicular to the plane as shown. Force on arm CD=ilB acting perpendicular to the plane as shown. These two forces constitute a couple on the coil. Moment of the couple = (Force) `xx` (Perpendicular distance between the forces) `= ilB (PQ sin theta)` Torque `=ilB b sing theta`. But `lxxb`= Area of coil `therefore" Torque "=iAB sin theta` If the loop has 'n' turns the troque on the coil `tau=n i AB sin theta` If `'phi'` is the deflection of the coil, that angle between the plane of the coil and magnetic field B `tau= n i AB cos phi` Moving coil galvanometer : Principle : When a current carrying coil is placed in the uniform magnetic field, it experiences a torque. Construction : i) It consists of a coil wound on a non metallic frame. ii) A rectangular coil is suspended between two concave shaped magnetic poles with the help of PHOSPHOUR Bronzee wire. iii) The lower portion of the coil is connected to a spring. iv) A small plane mirror M is fixed to the phosphour Bronze wire to measure the deflection of the coil. v) A small SOFT iron cylinder is placed with in the coil without touching the coil. The soft iron cylinder increases the induction field strength. vi) The concave shaped magnetic poles render the field radial. So maximum torque acting on it. vii) The whole of the apparatus is kept inside a brass case provided with a glass window.  Theory : Consider a rectangular coil of length l and breadth b and carrying current i suspended in the induction field strength B. Deflecting torque `(tau)=" B i A N" rarr (5)` where A= Area of the coil N = Total number of turns. The restoring torque developed in the suspension `=C theta rarr(2)` Where C is the couple PER unit twist and `theta` is the deflection made by the coil. When the coil is in equilibrium position Deflecting torque = Restoring torque `"B i A N "= C theta` `=((C)/("BAN"))theta` where `K=(C)/("BAN")=` Galvanometer constant. `i=K theta rarr (3)` `i prop theta` Thus delection of the coil is directly proportional to the current flowing through it. The deflection in the coil is measured using lamp and scale arrangement. |
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