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A charged particle moving in a magnetic ...

A charged particle moving in a magnetic field `vecB=hati-hatj` tesla, has an acceleration of `2hati+alpha hatj(m//s^(2))` at some instant. Find the value of `alpha`

Text Solution

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`vec(F) = q (vec(v) xx vec(B))`
`vec(a) = (q)/(m) (vec(v) xx vec(B))`
`rArr vec(a) bot vec(B)`
Thus `vec(a).vec(B) = 0`
`rArr (2 hat(i) + alpha hat(j)).(hat(i) - hat(j)) = 0`
`rArr 2 - alpha = 0`
`rArr alpha = 2`
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