2. A long straight wire carries a current of 150 A as shown below. A square coil

Question

2. A long straight wire carries a current of 150 A as shown below. A square coil with two sides parallel to the straight wire has sides 5 cm with the near side a distance 2 cm from the wire. The coil carries a current of 12 A. What is the net force on the coil? a) 0.0000714 N b) 0.000643 N c) 0.00532 N d) 0.0418 N 3. A cyclotron is designed for accelerating protons. The energy of the proton is 20 MeV and t magnetic field is 2.5 field, what is the radius of the cyclotron? a) 26 cm. b) 375 m. c) 5 cm. d) 26 km. 4. A small current clement 1 dl = 0.03 i (A m) is centered at the origin. What is the magnet field vector dB it produces at x=3m, y=0, z=0? a) zero. b) 1.88 x 10-6 k Tesla. c) 3.33 x 10-6 j Tesla. d) 1.88 x 10-10 k Tesla.

Explanation / Answer

here,

Use F = I L x B,

where I = Ib, L = 0.05 m, and

B = u0 * Ia / 2pi r

So the wire induces a B field that point inward into the screen,

and this induces a net force on the square loop only for the part of the square loop that is parallel to the long straight wire.

The part of the square loop that is perpendicular to the long wire has ZERO net force acting on it.

So for the part of the square loop that's closer to the wire, r = 0.02 m.

Bc = (4 * pi * 10^-7) (150) / 2 pi *(0.02) = 1.5 * 10^-3 T

For the part of the square loop that's further away from the wire, r = 0.07 m

B = (4 * pi * 10^-7) (150) / 2 pi *(0.07) = 4.29 * 10^-4 T

Now the net force acting on the square loo is:

F = (12) * ( 0.05) * ( 1.5 * 10^-3 T - 4.29 * 10^-4 )

F = 6.43 * 10^-4 N

F = 0.000643 N

the net force on the coil is b) 0.000643 N

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