A proton moves through a uniform magnetic field given by ModifyingAbove Upper B

Question

A proton moves through a uniform magnetic field given by ModifyingAbove Upper B With right-arrow equals left-parenthesis 14.9ModifyingAbove i With caret minus 32.7ModifyingAbove j With caret plus 24.9ModifyingAbove 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 1.74? 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 5.26times 10 Superscript negative 17 Baseline ? Upper Nright-parenthesis i Overscript caret EndScripts plus left-parenthesis 2.40times 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?

Explanation / Answer

B = (14.9 i - 32.7j + 24.9k)mT

v = ( vxi + vyj + 1.74 km/s k )

F = (5.26 x 10^-17i + 2.40 x 10^-17 j)

F = q[ v x B]

v x B = (0.0249vy + 56.898) i - ( 0.0249vx - 25.926)j + (-0.0327vx - 0.0149 vy) k

F = q( v x B)

q = 1.6 x 10^-19

now compare both side

vx = -4982.89 m/s

vy = 10917.751 m/s

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