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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, $\vec{B} = 1.13 \times 10^{- 15} T \hat{k}$

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.

${\vec{B}}_{point charge} = \frac{μ_{o}}{4 π} \frac{q v \sin θ}{r^{2}}$

02

Using Pythagorean Theorem

The distance $r$ between the proton and therefore the dot point by

$r = \sqrt{(1)^{2} + (1)^{2}} = \sqrt{2} cm$

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

$θ = \tan^{- 1} \frac{1 cm}{1 cm} = 45 °$

$θ = \tan^{- 1} \frac{1 cm}{1 cm} = 45 °$

03

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

the value for $θ, q, v$ and $r$ into equation to urge $\vec{B}$ by

$\vec{B} = \frac{μ_{o}}{4 π} \frac{q v \sin θ}{r^{2}}$

$= (\frac{4 π \times 10^{- 7} T \cdot m / A}{4 π}) (\frac{(1.6 \times 10^{- 19} C) (2 \times 10^{7} m / s) \sin 45 °}{{(\sqrt{2} \times 10^{- 2} m)}^{2}})$

$= 1.13 \times 10^{- 15} T$ $\hat{k}$

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Most popular questions from this chapter

Magnetic resonance imaging needs a magnetic field strength of 1.5 T. The solenoid is 1.8 m long and 75 cm in diameter. It is tightly wound with a single layer of 2.0-mm-diameter superconducting wire. What size current is needed?

FIGURE EX29.37 is a cross section through three long wires with linear mass density 50 g/m. They each carry equal currents in the directions shown. The lower two wires are 4.0 cm apart 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?

A $100 A$ current circulates around a $2.0 mm$ diameter superconducting ring.

a. What is the ring’s magnetic dipole moment?

b. What is the on-axis magnetic field strength $5.0 cm$ from the ring?

What magnetic field strength and direction will levitate the $2.0 g$ wire in FIGURE EX29.33?

A proton moves in the magnetic field $\vec{B} = 0.50 \hat{ı} T$ with a speed of $1.0 \times 10^{7} m / s$ in the directions shown in FIGURE. For each, what is magnetic force $\vec{F}$ on the proton? Give your answers in component form.

See all solutions

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