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A uniform magnetic field B=B(0)hatj exis...

A uniform magnetic field `B=B_(0)hatj` exists in space. A particle of mass m and charge q is projected towards X-axis with speed v from a point (a,0, 0). The maximum value of v for which the particle does not hit the Y-Z plane is

A

`(2Bq)/(dm)`

B

`(Bqd)/(m)`

C

`(Bq)/(2dm)`

D

`(Bqd)/(2m)`

Text Solution

Verified by Experts

The correct Answer is:
B
`R le d implies (mV)/(qB) le d`
`V le (Bqd)/(m) implies V_(max)=(Bqd)/(m)` .
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A uniform magnetic ficld B ы B_(0) j exists in space. A particle of mass m and charge q is projected towards negative x -axis with speed v from the a point (d, 0,0) . If the maximum value of v for which the particle does not hit y^(-z) plane is (4 B_(0) q d)/(alpha m) , then calculate alpha .

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Knowledge Check

  • A uniform electric field vecE in the y-direction and uniform magnetic field vecB in the x-direction exists in free space. A particle of mass m and carrying charge g is projected from the origin with speed v_0 along the y axis. The speed of the particle as a function of its y coordinate will be

    A
    `sqrt(v_(0)^(2)+(2qEy)/(m))`
    B
    `sqrt(v_(0)^(2)+(qEy)/(m))`
    C
    `sqrt(v_(0)^(2)+(4qEy)/(m))`
    D
    `v_(0)`

  • A plane metallic sheet is placed with its face parallel to lines of magnetic induction B of a uniform field. A particle of mass m and charge q is projected with a velocity v from a distance d from the plane normal to the lines of induction. Then, the maximum velocity of projection for which the particle does not hit the plate is

    A
    `2Bqd/m`
    B
    `Bqd/m`
    C
    `Bqd/2m`
    D
    `Bqd/d`

  • In a certain region of space, there exists a uniform and constant electric field of strength E along x-axis and uniform constant magnetic field of induction B along z-axis. A charge particle having charge q and mass m is projected with speed v parallel to x-axis from a point (a, b, 0). When the particle reaches a point 2a, b//2 , 0 its speed becomes 2v. Find the value of electric field strength of m, v and co-ordinates.

    A
    `3/2 (mv^2)/(qa)`
    B
    `(mv^2)/(qa)`
    C
    `(2mv^2)/(qBa)`
    D
    `3/2 vB`

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