kanwal32
  • kanwal32
A bullet of mass m and charge q is fired towards a solid uniformly charged sphere of radius R and total charge +q. If it strikes the surface of sphere with speed u, find the minimum value of u so that it can penetrates through the sphere
Physics
chestercat
  • chestercat
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kanwal32
  • kanwal32
|dw:1432973996650:dw|
kanwal32
  • kanwal32
kanwal32
  • kanwal32
help

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kanwal32
  • kanwal32
1mv^2/2=Kq^2/r
kanwal32
  • kanwal32
|dw:1432974143504:dw|
kanwal32
  • kanwal32
kanwal32
  • kanwal32
kanwal32
  • kanwal32
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  • kanwal32
IrishBoy123
  • IrishBoy123
it's a sphere of uniform charge so there is a field inside it: E = k q r / R^3 where r is measured out from centre of sphere see here: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesph.html the field will repel the bullet until/unless bullet reaches centre of sphere, then it will push the built out in the other direction. the bullet needs sifficient kinetic energy in order "work" it was to the centre of the sphere. yes? does that sound right?
kanwal32
  • kanwal32
can u give the soln
kanwal32
  • kanwal32
pls
IrishBoy123
  • IrishBoy123
W = F.x F = E.q \[W = \int\limits_{R}^{0} \frac{k \ q^2 \ r}{R^3} \ dr = - \frac{k \ q^2 }{R^3} \frac{R^2}{2} = - \frac{k \ q^2 }{2R}\] minus 'cos that is the energy the bullet will lose so -kq^2/2R + 1/2 m u^2 = 0 \[u = \sqrt{\frac{k q^2}{mR}}\] pls pls pls check algebra as i am actually trying to make breakfast here!! but that is "how" you could do it. key is that hyperphysics thing i linked
kanwal32
  • kanwal32
thnx same i was thinking
IrishBoy123
  • IrishBoy123
of course this assumes the charge sphere is made of jelly :p
kanwal32
  • kanwal32
yes no resistance
IrishBoy123
  • IrishBoy123
glad you agree. i clarification: "minus 'cos that is the **KE** energy the bullet will lose [ but the **PE** the bullet will gain**]" or looked at another way, that is the "work" the bullet will have to do, and the KE it will lose, in order to get to the centre of the sphere.

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