Problems applying Ampere’s law, using the vector notation

Problems applying Ampere’s law, using the vector notation

Subject: Physics    / Electricity and Magnetism
Question

1. A long wire parallel to the x axis carries a current of 6.5 A in the positive x direction. There is a uniform magnetic field B = 1.35 T j. Find the force per unit length on the wire.
2. A long straight wire carries a current of 50 A. An electron, traveling at 1.0 x 107 m/s, is 5.0 cm from the wire. What is the magnitude of the magnetic force on the electron if the electron velocity is directed?
(a) Toward the wire,
(b) Parallel to the wire in the direction of the current, and
(c) Perpendicular to the two directions defined by (a) and (b)

3. A 10-cm length of wire carries a current of 4.0 A in the positive z direction. The force on this wire due to a magnetic field B is F = (–0.2i + 0.2j) N. If this wire is rotated so that the current flows in the positive x direction, the force on the wire is F = 0.2k N. Find the magnetic field B.
4. A rectangular loop of wire with sides H = 30 cm and W = 65 cm carries current I2 = 0.383 A. An infinite straight wire, located a distance L = 34 cm from segment ad of the loop as shown, carries current I1 = 0.598 A in the positive y-direction.

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1)What is Fadx, the x-component of the force exerted by the infinite wire on segment ad of the loop?

2)What is Fbcx, the x-component of the force exerted by the infinite wire on segment bc of the loop?

3)What is Fnety, the y-component of the net force exerted by the infinite wire on the loop?

4)Another infinite straight wire, aligned with the y-axis is now added at a distance 2L = 68 cm from segment bc of the loop as shown. A current, I3, flows in this wire. The loop now experiences a net force of zero.

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What is the direction of I3?

5)What is the magnitude of I3?