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Question

Two identical particles having the same mass m and charges +q and q, separated by a distance d, enter in a uniform magnetic field B directed perpendicular to paper inward with speeds v1 and v2 as shown in the figure. The particles will not collide if

  1. d>mBq(v1+v2)
  2. d>mBq(v1+v2)
  3. d>2mBq(v1+v2)
  4. v1=v2


Solution

The correct option is C d>2mBq(v1+v2)
The particles +q and q will experience some force due to magnetic field and the direction of this force can be determined by Fleming's left hand rule. r1 and r2 are the radius of circular path followed by q and +q respectively.
To satisfy the condition of no collision
d>(2r1+2r2)
 d>2(mv1qB+mv2qB)
d>2m(v1+v2qB)
 

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