2. (40) A proton is moving with a velocity of -200i (to the left) along a long s

Question

2. (40) A proton is moving with a velocity of -200i (to the left) along a long straight wire with cu is 250 mA (to the right). At this instant, the proton's distance from the wire is 2.64 cm. -O proton (a) What is the acceleration of the proton? Express your answer in unit-vector notation. (b) Is the speed of the proton increasing, decreasing, or constant at this moment? Explain briefy. (c) What electric field will make the proton continue to travel in a straight line along the wire? Express your answer in unit-vector notation.

Explanation / Answer

a) magnetic field due to current carrying wire

B = Uo*i/(2*pi*d) = 4*pi*10^-7*250*10^-3/(2*pi*0.0264) = 1.89*10^-6 k T

=> force on proton , F = q(vxB) = 1.6*10^-19*(-200 i)*1.89*10^-6 k = 604.8*10^10^-25 j N

=> acceleration , a = F/m = (604.8*10^10^-25 j)/(1.67*10^-27) = 36.16*10^3 j m/s^2

b) speed of proton increasing . acceleration is positive

c) F = qE

=> electric field , E = F/q = 604.8*10^10^-25 j / (1.6*10^-19) = 378*10^-6 j N/C

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