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Chapter 29: Q. 23 (page 831)

The value of the line integral of B→around the closed path in FIGURE EX29.23 is 1.38×10-5T.m. What are the direction (in or out of the page) and magnitude of I3?

Short Answer

Expert verified

The current I3=23Aand it is points into the paper.

Step by step solution

01

Given information

We have given,

line integral =1.38×10-5T.m

We have to find the current I3and its flow of direction.

02

Simplify

Using ampere's law, for any closed path is given by,

∮B→.dS→=μ0I

Where I is a total enclosed current in the magnetic field curve.

then total current will be

I=I2+I3I=-12A+I3.......................(1)

since other currents are out of closed curve.

since,

∮B→.dS→=μ0I∮B→.dS→=(4π×10-7T.m/A)II=∮B→.dS→4π×10-7=1.38×10-5T.m4×3.14×10-7T.m/AI=11A

using equation (1),

localid="1649421657359" I=11A=-12A+I3I3=23A.

the positive sine indicates that current will be into the paper.

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Most popular questions from this chapter

a. In FIGURE P29.76, a long, straight, current-carrying wire of linear mass density μis suspended by threads. A magnetic field perpendicular to the wire exerts a horizontal force that deflects the wire to an equilibrium angle θ. Find an expression for the strength and direction of the magnetic field B⇀.

b. What B⇀deflects a 55 g/m wire to a 12° angle when the current is 10 A?

What are the magnetic fields at points a to c in FIG URE EX29.12? Give your answers as vectors.

A proton in a cyclotron gains ∆k=2e∆vof kinetic energy per revolution, where ∆vis the potential between the dees. Although the energy gain comes in small pulses, the proton makes so many revolutions that it is reasonable to model the energy as increasing at the constant rate p=dK/dt=∆K/T, where Tis the period of the cyclotron motion. This is power input because it is a rate of increase of energy.

a. Find an expression for r(t), the radius of a proton's orbit in a cyclotron, in terms of m,e,B,P,andt. Assume that r=0at t=0.

Hint:Start by finding an expression for the proton's kinetic energy in terms of r.

b. A relatively small cyclotron is 2.0min diameter, uses a 0.55Tmagnetic field, and has a 400Vpotential difference between the dees. What is the power input to a proton, in W?

c. How long does it take a proton to spiral from the center out to the edge?

FIGURE EX29.37 is a cross-section through three long wires with a linear mass density 50g/m. They each carry equal currents in the directions shown. The lower two wires are 4.0cmapart and are attached to a table. What current I will allow the upper wire to “float” so as to form an equilateral triangle with the lower wires?

The toroid of figureP29.55is a coil of wire wrapped around a doughnut-shaped ring (a torus). Toroidal magnetic fields are used to confine fusion plasmas.

a. From symmetry, what must be the shape of the magnetic field in this toroid? Explain.

b. Consider a toroid with N closely spaced turns carrying current I. Use Ampère’s law to find an expression for the magnetic field strength at a point inside the torus at distance r from the axis.

c. Is a toroidal magnetic field a uniform field? Explain.
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