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Chapter 22: Q14PE (page 811)

(a) Viewers of Star Trek hear of an antimatter drive on the Starship Enterprise. One possibility for such a futuristic energy source is to store antimatter-charged particles in a vacuum chamber, circulating in a magnetic field, and then extract them as needed. Antimatter annihilates with normal matter, producing pure energy. What strength magnetic field is needed to hold antiprotons, moving at\({\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{\rm{7}}}{\rm{ m/s}}\)in a circular path\({\rm{2}}{\rm{.00 m}}\)in radius? Antiprotons have the same mass as protons but the opposite (negative) charge. (b) Is this field strength obtainable with today鈥檚 technology or is it a futuristic possibility?

Short Answer

Expert verified

(a) The magnetic field strength is obtained as: \({\rm{0}}{\rm{.261 T}}\).

(b) The magnetic field strength is nowadays obtainable.

Step by step solution

01

Effect of magnetic field on the charged particle

When a charged particle moves in the presence of a magnetic field, a force acts on the mong charge particle given by Fleming鈥檚 right-hand rule and which deviates the path of the moving charged particle.

02

Production of the magnetic field

Nowadays the magnetic field in the laboratories is produced using electromagnets and a value of 2-3 T can be easily produced without many efforts, i.e., without the use of superconducting coils.

03

Evaluating the field strength(a)

To obtain the magnetic field strength for an anti-proton a particular circular path is followed.

The equation used is:\({\rm{r = }}\frac{{{\rm{mv}}}}{{{\rm{qB}}}}\).

Solving it for the value of\({\rm{B}}\)where the value of\({\rm{q}}\)is the antiproton鈥檚 charge and the value of\({\rm{m}}\)is the antiproton鈥檚 mass.

\(\begin{align}{}{\rm{B}}& = \frac{{{\rm{mv}}}}{{{\rm{qr}}}}\\ &= \frac{{\left( {{\rm{1}}{\rm{.67 \times 1}}{{\rm{0}}^{{\rm{ - 27}}}}\;{\rm{kg}}} \right){\rm{ \times }}\left( {{\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{\rm{7}}}{\rm{ m/s}}} \right)}}{{\left( {{\rm{1}}{\rm{.6 \times 1}}{{\rm{0}}^{{\rm{ - 19}}}}\;{\rm{C}}} \right){\rm{ \times }}\left( {{\rm{2}}{\rm{.00 m}}} \right)}}\\ &= {\rm{0}}{\rm{.261 T}}\end{align}\)

04

Explaining that Is this field strength obtainable with today’s technology or is it a futuristic possibility?(b)

The magnetic field strength is small and is easily obtainable these days.

Therefore, we get:

  1. The magnetic field strength is:\({\rm{0}}{\rm{.261 T}}\).
  2. The magnetic field strength is nowadays obtainable.

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Most popular questions from this chapter

One long straight wire is to be held directly above another by repulsion between their currents. The lower wire carries \({\rm{100 A}}\) and the wire\({\rm{7}}{\rm{.50 cm}}\) above it is \({\rm{10}}\)-gauge (\({\rm{2}}{\rm{.588 mm}}\) diameter) copper wire. (a) What current must flow in the upper wire, neglecting the Earth鈥檚 field? (b) What is the smallest current if the Earth鈥檚 \({\rm{3}}{\rm{.00 \times 10 - 5 T}}\) field is parallel to the ground and is not neglected? (c) Is the supported wire in a stable or unstable equilibrium if displaced vertically? If displaced horizontally?

The force on the rectangular loop of wire in the magnetic field in Figure 22.56 can be used to measure field strength. The field is uniform, and the plane of the loop is perpendicular to the field. (a) What is the direction of the magnetic force on the loop? Justify the claim that the forces on the sides of the loop are equal and opposite, independent of how much of the loop is in the field and do not affect the net force on the loop. (b) If a current of 5.00 A is used, what is the force per tesla on the 20.0-cm-wide loop?


Figure 22.56 A rectangular loop of wire carrying a current is perpendicular to a magnetic field. The field is uniform in the region shown and is zero outside that region.

Noting that the magnetic field lines of a bar magnet resemble the electric field lines of a pair of equal and opposite charges, do you expect the magnetic field to rapidly decrease in strength with distance from the magnet? Is this consistent with your experience with magnets?

Use the right-hand rules to show that the force between the two loops in Figure 22.49 is attractive if the currents are in the same direction and repulsive if they are in opposite directions. Is this consistent with like poles of the loops repelling and unlike poles of the loops attracting? Draw sketches to justify your answers.

Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
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