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(a) A circular current carrying coil has a radius R. Find magnetic field (a) at centre and (b) along the axis of coil distant sqrt(3) R from centre. The coil is having N turns and carriers a current i. (b) Two concentric coil A and B, having current i and 2i and radii 2R and R are placed as shown. Find magnetic field at common centre. (c) In previous problem, if planes of coil are perpendicular to each other, find magnetic field at common centre. (d) A charge q distributed uniformely over a circular ring of radius R. The ring rotates about its axis with an angular velocity omega. find the magnetic field (a) at centre and (b) at distance sqrt(3)R from centre, along the axis. |
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Answer» Solution :(a) (i) Magnetic FIELD at centre of coil `B_(C)=(mu_(0)NI)/(2R)` (ii) Magnetic field at point `P`, on the axis of coil at distance `x` from centre `B_(P)=(mu_(0)NIR^(2))/(2(R^(2)+x^(2))^(3//2))=(mu_(0)NiR^(2))/(2{R^(2)+(sqrt(3)R)^(2)}^(3//2))` `=(mu_(0)NiR^(2))/(2(4R^(2))^(3//2))=(mu_(0)NiR^(2))/(2xx2sqrt(2)R^(3))=(mu_(0)Ni)/(4sqrt(2)R)` (b)  At `O:` `B_(1)=(mu_(0)(2I))/(2R)=(mu_(0)i)/R, o.` `B_(2)=(mu_(0)i)/(2(2R))=(mu_(0)i)/(4R), ox` `B_(O)=B_(1)-B_(2)=(2mu_(0)i)/(4R), o.` (c) If planes of COILS are `bot^(ar)`, `B_(1)` and `B_(2)` will be `bot^(ar)`  `B_(O)=(mu_(0)i)/R sqrt((1)^(2)+1/((4)^(2)))` `=(sqrt(17)mu_(0)i)/(4R)` (d) Here current `i=q/T=q/(2pi//omega)=(qomega)/(2pi)` (i) `B_(C)=(mu_(0)i)/R=(mu_(0)q omega)/(4piR)` (ii) `B_(P)=(mu_(0)iR^(2))/(2[R^(2)+(sqrt(3)R)^(2)]^(3//2))` `=(mu_(0)iR^(2))/(4sqrt(2)R^(3))=(mu_(0)i)/(4sqrt(2)R)=(mu_(0)q omega)/(8sqrt(2) piR)` |
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