Question

A wire of length l carries a current i along the X-axis. A magnetic field exists which is given as $\vec { B } = B _ { 0 }$ ($\hat { i } + \hat { j } + \hat { k } )$ T. Find the magnitude of the magnetic force acting on the wire

• A.
• B. $\mathrm { B } _ { 0 } \mathrm { i } 1 \times \sqrt { 2 }$
• C.
• D.

Answer 1

Answer: (B)

$\mathrm { B } _ { 0 } \mathrm { i } 1 \times \sqrt { 2 }$

Answer 2

By using $\vec { F } = i ( \vec { l } \times \vec { B } )$

⇒

⇒

$\{ \hat { i } \times \hat { i } = 0 , \hat { i } \times \hat { j } = \hat { k } , \hat { i } \times \hat { k } = - \hat { j } \}$

It's magnitude $F = \sqrt { 2 } B _ { 0 } i l$