A proton moves through a uniform magnetic field given by ModifyingAbove Upper B With right-arrow equals left-parenthesis 10.5ModifyingAbove i With caret minus 21.6ModifyingAbove j With caret plus 22.1ModifyingAbove k With caret right-parenthesis mT. At time t1, the proton has a velocity given by v Overscript right-arrow EndScripts equals v Subscript x Baseline i Overscript caret EndScripts plus v Subscript y Baseline j Overscript caret EndScripts plus left-parenthesis 1.52? km/s right-parenthesis k Overscript caret EndScripts and the magnetic force on the proton is Upper F Overscript right-arrow EndScripts Subscript Upper B Baseline equals left-parenthesis 5.08times 10 Superscript negative 17 Baseline ? Upper Nright-parenthesis i Overscript caret EndScripts plus left-parenthesis 2.47times 10 Superscript negative 17 Baseline ? Upper Nright-parenthesis j Overscript caret EndScripts . (a) At that instant, what is vx? (b) At that instant, what is vy?
= (10.5 i - 21.6 j + 22.1 k) (10-3) T
= vx i + vy j + 1520 k
= (5.08 x 10-17) i + (2.47 x 10-17) j
q = charge on the proton = 1.6 x 10-19
magnetic force is given as
= q (x )
(5.08 x 10-17) i + (2.47 x 10-17) j = (1.6 x 10-19) (10-3) ((vx i + vy j + 1520 k) x (10.5 i - 21.6 j + 22.1 k))
(3.175 x 105) i + (1.54 x 105) j = ((-21.6 vx - 10.5 vy) k + (- 22.1 vx - 15960) j + (- 10.5 vy + 32832) i
comparing the coefficient of "j" both side
1.54 x 105 = - 22.1 vx - 15960
vx = -7690.5 m/s
comparing the coefficient of "k" both side
-21.6 vx - 10.5 vy = 0
-21.6 (-7690.5) - 10.5 vy = 0
vy = 15820.5 m/s
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