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(a) State Ampère's circuital law express...

(a) State Ampère's circuital law expressing it in the integral form.
(b) Two long coaxial insulated solenoids `S_(1) " and " S_(2)` of equal lengths are wound one over the other as shown in the figure. A steady current 'I' flows through the inner solenoid `S_(1)` , to the other end B which is connected to the outer solenoid `S_(2)` , through which the same current 'I' flows in the opposite direction so as to come out at end A. If `n_(1)" , and " n_(2)` are the number of turns per unit length, find the magnitude and direction of the net magnetic field at a point (i) inside on the axis and (ii) outside the combined system.

Text Solution

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(b) (i) The magnetic field due to solenoid `S_(1)` , is in upward direction and due to solenoid `S_(2)` , the magnetic field is in downward direction.
`n_(1) =` number of turns in solenoid `S_(1)`
`n_(2)` = number of turns in solenoid `S_(2)`
`B_(1) = mu_(0) n_(1) I`
`B_(2) = mu_(0)n_(2)I`
Net magnetic field `B = B_(1) - B_(2)`
` = mu_(0) n_(1) I - mu_(0) n_(2)I`
` = mu_(0)I (n_(1) - n_(2))` in upward direction
(ii) Magnetic field will be zero outside the system
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