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(a) Derive the expression for the torque acting on a current carrying placed in a magnetic field. (b) Explain the significance of a radial magnetic when current carrying coil is kept in it. |
Answer» Solution : Let us consider a rectangular coil ABCD carrying I, Placed in a magnetic FIELD B making an angle `theta` with the plane of the coid and `phi` with the area vector of the plane. `vec(F_(b))=vec(-F_(b))` `vec(F_(I))=vec(-F_(I))` So, they cancel out in pairsbut `vecF_(l)" and "vec(-F_(I))` provide torque to the ractangular coil ABCD. `tau="(Force )(Arm of Couple)"` `tau="Force"xx"Perpendicular distance between two action lines of forces"` `tau=I l B xx b cos theta` `tau=IlB b sin phi` let the number of turns be N `{:(tau="NIA B sin "phi,"{l" xx b=A),(tau="MB sin "phi, "NIA = M"):}""{{:(theta+phi=90^(@)),(theta=90^(@)-phi),(costheta=sinphi):}` Magnetic diploe moment `vec(tau)=vec(M)xxvec(B)`  Significance of radical magnetic field : When apply radical field as shown in the FIGURE `phi` is always equalsto `90^(@)`. `tau=MB sin 90^(@)` `sin 90^(@)=1` Hence, Torque MAXIMUM and constant. |
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