Present all of your work as clearly and neatly as possible. Please draw a box ar

Question

Present all of your work as clearly and neatly as possible. Please draw a box around your final answer. If you consistently and correctly show all units throughout a problem, you will get one bonus point for that problem. If your significant figures are correct throughout a problem, you will get an additional bonus point. A proton is moving with a velocity of upsilon = -200 m/8 (downward) toward a long straight wire with current i = 250mA (to the right). At this instant, the proton's distance from the wire is d = 2.64cm. What is the acceleration of the proton? Express your answer in unit-vector notation. Is the speed of the proton increasing, decreasing, or constant at this moment? Explain briefly.

Explanation / Answer

at a distance d = 2.64 = 0.0264 m

the magnitude of the magnetic field is B = mu_o*i/(2*pi*r) = (4*3.142**10^-7*250*10^-3)/(2*3.142*0.0264)

mu_o = 4*pi*10^-7 H/m

i = 250 mA = 250*10^-3 A

r = d = 0.0264 m

B = (4*3.142**10^-7*250*10^-3)/(2*3.142*0.0264) = 18.93 k hat

v = -200 j hat

then magnetic force F = q* (v X B)

v X B = -200 j hat X 18.93 k hat = -3787.87 i hat

q is the charge of the electron = 1.6*10^-19 C

then F = (1.6*10^-19*3787.87 i hat) = -6060.6*10^-19 i hat

but F =m*a

accelaration a = F/m = -(6060.6*10^-19 i hat )/(9.11*10^-31) =-665.3*10^12 i hat m/s^2

B) since accelaration is negative then speed of the proton is decreasing

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