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Question

In the x-y-plane, the region y>0 has a uniform magnetic field B1^k and the region y<0 has another uniform magnetic field B2^k. A positively charged particle is projected from the origin along the positive y-axis with speed Vo=πms1 at t=0, as shown in the figure. Neglect gravity in this problem. Let t=T be the time when the particle crosses the x-axis from below for the first time. If B2=4B1, the average speed of the particle, in ms1, along the x-axis in the time interval T is ________.

904061_0e7fb7d08aa44df2a13bdb35141fa502.png

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Solution

Average speed along the x-axis
(Vx)=|Vx|dtdt=d1+d2t1+t2 (1)
We also have,
r1=mvqB1,r2=mvqB2
since B1=B24
r1=4r2 (2)
Time in B1πBqB1=t1
Time in B2πBqB2=t2
Total distance along x-axis d1+d2=2r1+2r2=2(r1+r2)=2(5r2)
Total time T=t1+t2=5t2
Average speed =10r25t2=2mvqB2×qB2πm=2
828607_904061_ans_3a2974c55a994f7396ccaef5377da0e3.png

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