question_answer

A conducting wire bent in the form of a parabola\[{{y}^{2}}=2x\]carries a current \[i=2A\]as shown in figure. This wire is placed in a uniform magnetic field \[\overset{\to }{\mathop{B}}\,=-4\hat{k}\]tesla. The magnetic force on the wire (in newton)

A) \[-16\hat{i}\]

B) \[32\hat{i}\]   

C) \[-32\hat{i}\]

D) \[16\hat{i}\]

Correct Answer: B

Solution :

[b] At \[x=2\], \[{{y}^{2}}=2x=2\times 2\] or \[y=2\] Thus separation, \[AB=4\,cm\] The force, \[F=Bi\,(AB)\] \[=4\times 2\times 4=32\,N.\]