A wire of length 2 ~m carries a current of 1 ~A along the x axis. A magnetic field B=B₀(i+j+k) tesla exists in space. The magnitude of magnetic force on the wire is

Step-by-step solution

The magnetic force on a current-carrying wire is given by the formula F = I( L B ) . The length vector L of the wire is 2 i m, as it lies along the x-axis and has a length of 2 m. The current I is 1 A. The magnetic field is given as B = B₀( i + j + k ) . Substituting these values into the force equation: F = 1 (2 i ) B₀( i + j + k ) F = 2B₀ [( i i ) + ( i j ) + ( i k )] Using the cross product properties i i = 0 , i j = k , and i k = - j : F = 2B₀ [0 + k - j ] = 2B₀( k - j ) The magnitude of the force is | F | = |2