Question

If $\overrightarrow{J}=\frac{1}{r^3}(2cos\theta \widehat{a_r}+sin\theta \widehat{a_{\theta }})A/m^{2}0<\theta <\frac{\pi }{2},0<\varphi <2\pi$, then the current passing through hemispherical shell of radius 20 cm is _________A.

• A. 31.41

Answer 1

The correct option is A 31.41
As we know, $I=\int \int \overrightarrow{J}.\overrightarrow{ds}$

$\overrightarrow{ds}=r^{2}sin\theta .d\theta d\varphi a_r,$ because in this case as 'r' is fixed so dr = 0

$I={\int }_{\theta =0}^{\pi /2}{\int }_{\varphi =0}^{2\pi }\frac{1}{r^3}.2cos\theta r^{2}sin\theta .d\theta .d\varphi {|}_{r=0.2}$

$I=\frac{10\pi }{2}\times [cos0-cos\pi ]=10\pi Amp=31.4159Amp$