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Q.

In the xy-plane, the region y>0  has a uniform field B1k  and the region y<0  has another uniform magnetic field B2k . A positively charged particle is projected from the origin along positive y-axis with speed υ0=πs1 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 _______

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answer is 2.

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Detailed Solution

(i) Average speed along x-axis

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(ux)=|ux|dxdx=d1+d2t1+t2
(ii) We have,
r1=mυqB1,r2=mυqB2
Since,  B1=B24
r1=4r2
Time in  B1πmqB1=t1
Time in  B2πmqB2=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=2ms-1

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In the xy-plane, the region y>0  has a uniform 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 positive y-axis with speed υ0=πs−1 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 ms−1 , along the x-axis in the time interval T is _______