A charged particle with charge `q` enters a region of constant, uniform and mututally orthogonal fields `vec(E) and vec(B)` with a velocity `vec(v)` perpendicular to both `vec(E) and vec(B)`, and comes out without any change in magnitude or direction of `vec(v)`. Then
A
`vec(v) = vec(B) xx vec(E) //(vec(E)^(2))`
B
`vec(v) = vec(E) xx vec(B) //(vec(B)^(2))`
C
`vec(v) = vec(B) xx vec(E) //(vec(B)^(2))`
D
`vec(v) = vec(E) xx vec(B) //(vec(E)^(2))`
Text Solution
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The correct Answer is:
B
Here, ` vec(E) and vec(B)` are perpendicular to each other and the velocity ` vec(v)` does not change, therefore `qE = qvB rArr v= (E)/(B)` Also, | (vec(E) xx vec(B))/(B^(2))| = (E B sintheta)/(B^(2)) = (E B sin 90^(@))/( B^(2)) = (E)/(B) = | vec(v)| = v`
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