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Chapter 29: Q. 6 (page 830)

What is the magnetic field at the position of the dot in FIGURE. Give your answer as a vector.


Short Answer

Expert verified

The Magnetic field,B→=1.13×10-15Tk^

Step by step solution

01

Introduction

The source of a field is the moving charge. The Biot-Savart law is used to calculate the flow at a given degree. Because of radial and route length directions are always at right angles, the vector is doubled. Equation gives the magnetic flux due to the moving charge.

B→point charge=μo4πqvsinθr2

02

Using Pythagorean Theorem

The distance rbetween the proton and therefore the dot point by

r=(1)2+(1)2=2cm

The angle between the proton direction and therefore the real number is calculated by

θ=tan-11cm1cm=45°

θ=tan-11cm1cm=45°

03

Using the right-hand rule, locate the force field.

the value for θ,q,vand rinto equation to urgeB→by

B→=μo4πqvsinθr2

=4π×10-7T·m/A4π1.6×10-19C2×107m/ssin45°2×10-2m2

=1.13×10-15Tk^

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Most popular questions from this chapter

Although the evidence is weak, there has been concern in re-cent years over possible health effects from the magnetic fields generated by electric transmission lines. A typical high-voltage transmission line is20m above the ground and carries a 200A current at a potential of110KV.

a. What is the magnetic field strength on the ground directly under such a transmission line?

b. What percentage is this of the earth’s magnetic field of50μT?

The microwaves in a microwave oven are produced in a special tube called a magnetron. The electrons orbit the magnetic field at 2.4GHz, and as they do so they emit 2.4GHzelectro-magnetic waves.

a. What is the magnetic field strength?

b. If the maximum diameter of the electron orbit before the electron hits the wall of the tube is2.5cm, what is the maximum electron kinetic energy?

A square current loop 5.0cmon each side carries a500mA current. The loop is in a 1.2T uniform magnetic field. The axis of the loop, perpendicular to the plane of the loop, is 30°° away from the field direction. What is the magnitude of the torque on the current loop?

The two insulated wires in FIGUREP29.42cross at a 30∘angle but do not make electrical contact. Each wire carries a 5.0Acurrent. Points1and 2are each 4.0cm from the intersection and equally distant from both wires. What are the magnitude and direction of the magnetic fields at points1and2?

FIGUREP29.42 FIGUREP29.43

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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