Question

A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,(a) the wire intersects the axis,(b) the wire is turned from N-S to northeast-northwest direction,(c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?

Answer 1

(a)$l=2r=0.2;\theta ={90}^o$

$F=BiLsin\theta =2.1N$ acts on wire in a vertically downward.

(b)$l_1=l/sin\theta ;\theta ={45}^o$

$F=BiLsin\theta =2.1N$

2.1N acts vertically downward direction.

(c)Lowered from the axis by distance $d=6.0cm$

$(\frac{l_2}{2}{)}^2=4(d+r)=4\times 16c{m}^2\Rightarrow l_2=0.16m$

$F_2=Bi{l}_2=1.68N$ vertically downward direction.