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Problem 19 Easy Difficulty

Fusion Reactor. If two deuterium nuclei (charge $+e$ . mass $3.34 \times 10^{-27} \mathrm{kg}$ ) get close enough together, the attraction of the strong nuclear force will fuse to make an isotope of helium, releasing vast amounts of energy. The range of this force is about $10^{-15} \mathrm{m}$ . This is the principle behind the fusion reactor. The deuterium nuclei are moving much too fast to be contained by physical walls, so they are confined magnetically. (a) How fast would two nuclei have to move so that in a head-on collision they would get close enough to fuse? (Treat the nuclei as point charges, and assume that a separation of $1.0 \times 10^{-15}$ is required for fusion, $)$ (b) What strength magnetic field is needed to make deuterium nuclei with this speed travel in a circle of diameter 2.50 $\mathrm{m} ?$

Answer

a. $1.2 \times 10^{7} \mathrm{m} / \mathrm{s}$
b. $0.10 \mathrm{T}$

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Video Transcript

let's apply conservation of energy. But according to conservation affinity total initial energy which is K one place you one is equal to total final energy which is gate to bliss. You too Here you want is equal to key to is equal to zero and therefore K one is equal to you too. Well, there are two nuclei having equal kinetic energy. Therefore we have hahf m we square this Oh m Lee Square is equal to and time So we squared divided by R So in times um m times East were in fact, in onto the screen in times he squared divided by I'll write its energy. No, um from here we is equal to we musical to e times route key divided by m times are no let's like in numbers. So by doing substitution three is equal to one point 602 times 10 to the power minus 19 into route 8.99 times 10 to the power nine, divided by 3.3 fuller multiply by 10 to the power minus 27 multiplied by 1.0 times 10 to the dollar, minus 15 minus 15. Right, So we is equal to 8.3 times tend to give our six. I mean apart. Second, no, we do part B. Well, some of forces is equal to mance times X relation kyung times we be, which is magnetic force is equal to M weeks where divided by r and from here the is equal to m times we divided by Q times are so we have 3.34 times 10 to the dollar, minus 27 multiplied by eight wine three times 10 to the dollar. Six divided by 1.602 times 10 to the dollar minus 19 um, multiplied by 1.25 So magnetic field B is equal to Was it a point to 14 Tesla?

Top Physics 102 Electricity and Magnetism Educators
Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Meghan M.

McMaster University

Physics 102 Electricity and Magnetism Bootcamp

Lectures

Join Bootcamp