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Chapter 22: Q86PE (page 815)

A charged particle having mass \({\rm{6}}{\rm{.64 \times 1}}{{\rm{0}}^{{\rm{ - 27}}}}{\rm{\;kg}}\) (that of a helium atom) moving at \({\rm{8}}{\rm{.70 \times 1}}{{\rm{0}}^{\rm{5}}}{\rm{\;m/s}}\) perpendicular to a \({\rm{1}}{\rm{.50 - T}}\) magnetic field travels in a circular path of radius \({\rm{16}}{\rm{.0\;mm}}\).(a)What is the charge of the particle?(b)What is unreasonable about this result?(c)Which assumptions are responsible?

Short Answer

Expert verified
  1. The charge of the particle is \({\rm{2}}{\rm{.41}} \times {\rm{1}}{{\rm{0}}^{{\rm{ - 19}}}}\;{\rm{C}}\).
  2. Theunreasonableobjects must have charges that are integer multiples of the electrical charge.
  3. The radius specified does not match the other specifications.

Step by step solution

01

Concept Introduction

The area of space near a magnetic body or a current-carrying body where magnetic forces caused by the body or current can be detected.

02

Find the value of the charged particle

(a)

The equation\({\rm{r = }}\frac{{{\rm{mv}}}}{{{\rm{qB}}}}\)gives the radius of the curved route in terms of the charge; Apply this equation with the supplied numbers to solve for\({\rm{q}}\).

\(\begin{aligned}{}{\rm{q}} &= \frac{{{\rm{mv}}}}{{{\rm{rB}}}}\\ &= \frac{{\left( {{\rm{6}}{\rm{.64 \times 1}}{{\rm{0}}^{{\rm{ - 27}}}}{\rm{\;kg}}} \right){\rm{ \times }}\left( {{\rm{8}}{\rm{.70 \times 1}}{{\rm{0}}^{\rm{5}}}\;{\rm{m/s}}} \right)}}{{\left( {{\rm{16}}{\rm{.0 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}\;{\rm{m}}} \right){\rm{ \times }}\left( {{\rm{1}}{\rm{.50\;T}}} \right)}}\\ &= {\rm{2}}{\rm{.41 \times 1}}{{\rm{0}}^{{\rm{ - 19}}}}\;{\rm{C}}\end{aligned}\)

Therefore,The charge of the particle is \({\rm{2}}{\rm{.41 \times 1}}{{\rm{0}}^{{\rm{ - 19}}}}\;{\rm{C}}\).

03

Explaining the unreasonable result

(b)

When you divide the charge in component\({\rm{2}}{\rm{.41 \times 1}}{{\rm{0}}^{{\rm{ - 19}}}}\;{\rm{C}}\)by the electronic charge, you get

\(\frac{{{\rm{2}}{\rm{.41 \times 1}}{{\rm{0}}^{{\rm{ - 19}}}}\;{\rm{C}}}}{{{\rm{1}}{\rm{.60 \times 1}}{{\rm{0}}^{{\rm{ - 19}}}}\;{\rm{C}}}} = \frac{{\rm{3}}}{{\rm{2}}}\)

Objects must have charges that are integer multiples of the electrical charge.

04

Explaining which assumptions are responsible

(c)

The radius in question does not fit with the other parameters to provide a suitable charge value.

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Most popular questions from this chapter

An inventor wants to generate \({\rm{120 - V}}\) power by moving a \({\rm{1}}{\rm{.00 - m - long}}\) wire perpendicular to the Earth's \({\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{\;T}}\) field. (a) Find the speed with which the wire must move. (b) What is unreasonable about this result? (c) Which assumption is responsible?

A 200-turn circular loop of radius50.0cmis vertical, with its axis on an east-west line. A current of 100 A circulates clockwise in the loop when viewed from the east. The Earth's field here is due north, parallel to the ground, with a strength of 3.00脳10鈥�5T. What are the direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?

An AC appliance cord has its hot and neutral wires separated by 3.00mmand carries a5.00-A current. (a) What is the average force per meter between the wires in the cord? (b) What is the maximum force per meter between the wires? (c) Are the forces attractive or repulsive? (d) Do appliance cords need any special design features to compensate for these forces?

What is the direction of the velocity of a negative charge that experiences the magnetic force shown in each of the three cases in Figure22.51, assuming it moves perpendicular to B?

(a) A physicist performing a sensitive measurement wants to limit the magnetic force on a moving charge in her equipment to less than1.00脳10鈥�12N. What is the greatest the charge can be if it moves at a maximum speed of30.0m/sin the Earth鈥檚 field? (b) Discuss whether it would be difficult to limit the charge to less than the value found in (a) by comparing it with typical static electricity and noting that static is often absent.
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