Question

**Note:** I'm really only struggling with part
c.

Lorentz Law, Ampere's Law, and Faraday's Law

a.) Two equal current carrying infinite wires with current I = 2amps and separation d = 0.5m repel one another. Find the force per unit lengh (f). Give the relative directions of the currents in the wires by drawing a diagram.

b.) Find the strength of the magnetic field (B) inside a solenoid with n= 200 turns/meter (loops per unit length) and carrying a current of I = .06amps.

c.) Suppose that the solenoid in part (b) has a radius (a = 10cm) and a changing current of I = (0.4 + 0.5t)amps, where t is the time. Another metallic ring of radius b = 7cm is placed inside of the solenoid with their axes coinciding. Find the EMF (E) induced in the ring.

Answer #1

a) This can be solved using the following formula

F/l = u_{o}I_{1}I_{2} / 2*pi*r

where I_{1} and I_{2} are currents in wire which
is 2 amps in this case. r is the distance between two wires.

b) Here you can use the following formula

B = u_{o}In

Putting the values, we het

B = 4*pi*10^{-7}*0.06*200

B = 1.507e-5 Tesla

c) We know that Induced emf is given as

e = -N d(phi)/ dt where phi = B*A

from part (b) , phi = u_{o}In*pi*r^{2}

e = - N*u_{o}In*pi*r^{2}*dI/dt

e = - N*u_{o}In*pi*r^{2}d(0.4 + 0.5t)
/ dt

e = -N*u_{o}*I*n*pi*r^{2}*0.5

we are not given number of turns of ring so take N = 1

r = 0.07 m

solve for e

e =

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