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Current and Magnetic Field So far we have seen that when a moving charge or current in a conductor is exposed to a uniform magnetic field, it experiences a force. 1 Lightning Revisited Lightning bolts carry ~200 C of charge. 2 Current and Magnetic Field So far we have seen that when a moving charge or current in a conductor is exposed to a uniform magnetic field, it experiences a force. We have also seen that when a current loop is exposed to a magnetic field, it experiences a torque. This torque can be expressed in the general form: = x B where =I A is the magnetic moment 3 Magnetic Moment The magnetic moment is a vector whose direction is obtained from the direction of the current, using the right hand rule: =I A I 4 Magnetic Moment The magnetic moment is a vector whose direction is obtained from the direction of the current, using the right hand rule: I I 5 Magnetic Moment on a current coil A coil is a loop with more than one turn In this case, each turn feels the torque for one loop If there are N turns, the torque will multiply N fold. = N I Ax B If we still write = xB Then the magnetic moment of the coil is: = N I A 6 Example 22.5 : Torque on a current coil Dimensions 5.4cm x 8.5 cm N = 25 turns I = 15 mA B =0.35 T parallel to the plane of the loop. 7 Biot Savart Law: Magnetic field due to an electric current Question: what is the origin of the magnetic field ? Observation of Biot and Savart: A current carrying conductor gives rise to a magnetic field around it. You have done the same experiment in your last lab. d B=k m Id s x r r observation point P 2 r I d s 8 Electric field due to an electric charge An analogous question to : what is the origin of the electric field ? dq d E=k e 2 r 1 1 k e= 4 0 epsilon-zero is the permittivity of free space 9 Biot Savart Law: Magnetic field due to an electric current Question: what is the origin of the magnetic field ? Observation of Biot and Savart: A current carrying conductor gives rise to a magnetic field around it. You have done the same experiment in your last lab. d B=k m Id s x r r 2 0 k m=10 T.m/ A= 4 7 mu-zero is the permeability of free space 10 Biot Savart Law: Magnetic field due to an electric current Simplify: consider the magnetic field at an axial point above a current loop. d B=k m Id s x r r I 0 I d s dB= 4 x2 R2 2 P r x R r d s do in class 11 Biot Savart Law: Magnetic field due to an electric current Simplify: an infinite conductor d B=k m Id s x r r observation point P 2 r I r d s do in class 12