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JEE MainPhysicsMagnetic Effects of Current

A particle having a positive charge of 2 C moves along the z-axis with a velocity v = 2 k m s ⁻¹ . It enters a region containing a uniform magnetic field given by B = B_x i + 3 j T . If the magnetic force experienced by the particle is F = -12 i + 16 j N , then the value of B_x is ____.

Correct answer

4

Step-by-step solution

The magnetic force on a moving charge is given by F = q( v B ) . Substitute the given values into the formula: F = 2(2 k (B_x i + 3 j )) Evaluate the cross product: v B = 2B_x( k i ) + 6( k j ) Using the properties of unit vectors, k i = j and k j = - i : v B = 2B_x j - 6 i Now multiply by the charge q = 2 C : F = 2(2B_x j - 6 i ) = -12 i + 4B_x j We are given that F = -12 i + 16 j N . Comparing the j components of the calculated and given force vectors: 4B_x = 16 B_x = 4 Answer: 4

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