Solenoids produce magnetic fields that are relativelyintense for the amount of c

Question

Solenoids produce magnetic fields that are relativelyintense for the amount of current they carry. To make a directcomparison, consider a solenoid with 57 turns per centimeter, aradius of 1.05 cm, and a current of 0.144 A. Calculate the magneticfield at the center of the solenoid.
What current must a long, straight wire carry tohave the same magnetic field as that found above? Let the distancefrom the wire be the same as the radius of the solenoid, 1.05cm.
What current must a long, straight wire carry tohave the same magnetic field as that found above? Let the distancefrom the wire be the same as the radius of the solenoid, 1.05cm.

Explanation / Answer

   a.   Magnetic field at thecenter of solenoid   B   =   0* n * I    n   =   no. ofturns per unit length   =   57 / 1cm   =   5700   /m       B   =   4* * 10-7 * 5700 *0.144   =   1.03 *10-3   T    b.   Magnetic field due to along wire   B   =   0* I' / 2 * * r    r   =   1.05 cm   =   0.0105   m          1.03 *10-3   =   4 * 3.14 *10-7 * I' / 2 * 3.14 * 0.0105       Requiredcurrent      I'   =   0.0105* 1.05 * 10-3 / 2 *10-7   =   55.1   A       

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