Two point charges are aligned along the x-axis as show in the above figure (righ

Question

Two point charges are aligned along the x-axis as show in the above figure (right). The charges are as follows q_A = 4.0 nC and q_B = 3.0 nC. (a) Find the electric field due to charge A at x = 0.4 m. (b) Find the electric field due to charge B at x = 0.4 m. (c) If a charge of 5.0nc is placed at x = 0.4 m. Determine the electric force acting on it. (Include the direction of the force.) A solenoid 10 cm in diameter and 630 cm long is made from copper wire of diameter 0.050 cm, with very thin insulation. The wire is wound onto a cardboard tube to make a solenoid. (a) Determine the resistance in the wire. You may take the resistivity of copper to be 1.68 times 10^-8 Ohm m. (b) The number of turns in the wire is ten. Find the current necessary to produce a magnetic field of strength 1.5 T. (c) How much power is needed to produce the magnetic field?

Explanation / Answer

Given

solenoid of 10 cm = 0.1m diameter , radius R_s = 0.05 m

and length L = 630 cm = 6.3 m

copper wire of diameter d = 0.050 cm ==> radius is r = 0.025 m

a) resistivity of copper is rho =R*A/l ==> R = rho*l/A = (1.68*10^-8*6.3)/(pi*0.025^2) ohm = 5.3903*10^-5 ohm

  
b) N=10 ,B = 1.5 T

   we know that the magnetic field of a solenoid is B = mue0*N*i/l

              
           B = mue0*N*i/l
           i = B*l/(mue0*N)
          
           i = 1.5*6.3/(4pi*10^-7*10) A

           i = 752007 A

c) the power need to produce the magnetic field is P = i^2*R = 752007^2*5.3903*10^-5 W = 30482929.61 W

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