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A proton moves through a region of space where there is a magnetic field B⃗ =(0.57i+0.37j)T...

A proton moves through a region of space where there is a magnetic field B⃗ =(0.57i+0.37j)T and an electric field E⃗ =(2.7i−4.0j)×103V/m. At a given instant, the proton's velocity is v⃗ =(7.0i+2.8j−4.9k)×103m/s.

Determine the components of the total force on the proton.

Fx, Fy, Fz =

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Answer #1

electric force Fe = q*E

magnetic force Fm = q*(v x B)

total force F = Fe + Fm

F = q*(E + vxB)

vxB = ( (7i + 2.8j - 4.9k) x (0.57i + 0.37j) = 7*0.37 k - 2.8*0.57 k - 4.9*0.57 j + 4.9*0.37 i ) * 10^3

v x B = ( 0.994 k - 2.79 j + 1.81 i ) * 10^3

E + vxB = ( (2.7 + 1.81) i + (-4-2.79) j + 0.994 k ) * 10^3

E + vxB = (4.51i - 6.79j + 0.994k)*10^3

F = q*(E + vxB) = (7.21i - 10.86j + 1.59k)*10^(-16) N

Fx = 7.21*10^(-16) N

Fy = - 10.86*10^(-16) N

Fz = 1.59*10^(-16) N

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