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Write the expression for the force vecF ...

Write the expression for the force `vecF` acting on a particle of charge q moving with a velocity `vecv` in the prensnece of both electric field `vecE` and magnetic field `vecB`. Obtain the condition under which the particle moves undeflected through the fields.

Text Solution

Verified by Experts

1st Part : Force
`vecF= vecF_(e) +vecF_(m)= qvecE+ qvecvxx vecB=q(vecE+vecv xx vecB)`
2nd Part : The required condition is either, `vecF=0`, i., ono resultant force acts on the particle. In that case, `vecE=-qvecvxx vecB`.
or, `vecE and vecB` are both along the direction of velocity of the particle, of motion produces a constant acceleration without any deflection.
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Knowledge Check

  • A particle with charge q is moving with a velocity vecv in a magnetic field vecB . If the force acting on the particle is vecF then,

    A
    `vecF=0`, when `vecv` and `vecB` are parallel
    B
    magnitude of `vecF` is maximum when `vecv` and `vecB` are perpendicular to each other
    C
    `|vecF|=(1)/(2)qvB` when the angle between `vecv` and `vecB` is `45^(@)`
    D
    direction of `vecF` remains the same when the directions of both `vecv` and `vecB` are reversed simultaneously

  • A charge particle travels along a straight lines with a speed nu in a region where both electric field E and magnetic field B are present it follows that

    A
    `absE=nu absB` and the two fields are parallel
    B
    `absE=nu absB` and the two fields are perpendicular
    C
    `absB= nu absE` and the two fields are parallel
    D
    `absB= nu abs E` and two fields are perpendicular

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