Question

Consider a straight conductor of length 2m. Carrying a current of 10 A in the +z direction. If the conductor is placed in a field of $\overrightarrow{B}=0.02({\hat{a}}_y-{\hat{a}}_x)Wb/m^2$ , then the force on per unit length of the conductor is

• A. $-0.4({\hat{a}}_x+{\hat{a}}_y)N/m$
• B. $-0.4({\hat{a}}_x-{\hat{a}}_y)N/m$
• C. $-0.2({\hat{a}}_x+{\hat{a}}_y)N/m$
• D. $0.2({\hat{a}}_x+{\hat{a}}_y)N/m$

Answer 1

The correct option is C $-0.2({\hat{a}}_x+{\hat{a}}_y)N/m$

(c)
$\overrightarrow{F}=I(\overrightarrow{L}\times \overrightarrow{B})$

= 10($2{\hat{a}}_z\times 0.02({\hat{a}}_y-{\hat{a}}_x)$

= $10\left(0.04\right(-{\hat{a}}_x)-0.04{\hat{a}}_y)$

= $-0.4{\hat{a}}_x-0.4{\hat{a}}_y$
Force acting per unit length,

$\frac{\overrightarrow{F}}{L}=\frac{-0.4{\hat{a}}_x-0.4{\hat{a}}_y}{2}$

= $-0.2{\hat{a}}_x-0.2{\hat{a}}_y$

$\frac{\overrightarrow{F}}{L}$ = $-0.2({\hat{a}}_x+{\hat{a}}_y)$