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JEE MainPhysicsMagnetic Effects of Current

A straight wire segment carrying a steady current is placed in a uniform magnetic field. The wire is represented by the length vector L = (2 i + 3 j ) m . If the magnetic force experienced by the wire is F = (3 i - j + 4 k ) N , then the value of is

Options

  1. A-2
  2. B4
  3. C3
  4. D2

Correct answer

D. 2

Step-by-step solution

The magnetic force on a straight current-carrying wire is given by F = I( L B ) . From the properties of the cross product, the magnetic force vector F must be perpendicular to the length vector L . Therefore, their dot product must be zero: F L = 0 Substituting the given vectors: (3 i - j + 4 k ) (2 i + 3 j ) = 0 (3)(2) + (- )(3) + (4)(0) = 0 6 - 3 = 0 = 2 Answer: 2

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