For a positively charged particle moving in a `x-y` plane initially along the `x-axis` , there is a sudden change in its path due to the presence of electric and//or magnetic fields beyond `p` . The curved path is shown in the ` x- y `plane and is found to be non - circular. Which one of the following combinations is possible ?
A
` vec(E) = 0 , vec(B) = b hat(i) +chat(k)`
B
` vec(E) = a hat(i) , vec(B) = c hat(k) +a hat(i)`
C
` vec(E) = 0 , vec(B) = c hat(j) + b hat(k)`
D
` vec(E) = a hat (i) , vec(B) = bc hat(k) +b hat(j)`
Text Solution
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The correct Answer is:
B
The velocity at `P` is in the ` x- directiomn` ( given) . Let vec(v) = k hat(i)`. After `p`, the positively charged particle gets deflected in the ` x- y ` plane toward - y direction and the path is non - circular . Now , ` vec(F) = q (vec(v)xx vec(B)` rArr vec(F) = q [ k hat (i)xx(c hat (k) + a hat (i))]` for option (b) ` = q [kc hat(i) xx hat(k) + hat(k) a hat(i) xx hat (i)] = kcq hat(-j)` since in option (b) , electric field is also present ` vec (E) - a hat (i) , therfore it will also exert a force in the ` + X direction` . The net result of the two forces will be a non - circular path . Only option (b) fits for the above logic . For other option , we get some other results.
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