What should be the current i (in A) in a circ | vedclass

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(B) The magnetic field at the center of a circular coil is given by $B = \frac{{\mu_0 i}}{{2r}}$.Given,$\mu_0 = 4\pi 	imes {10^{ - 7}}\,T\cdot m/A$,$

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) The magnetic field at the center of a circular coil is given by $B = \frac{{\mu_0 i}}{{2r}}$.Given,$\mu_0 = 4\pi 	imes {10^{ - 7}}\,T\cdot m/A$,$r = 5\,cm = 5 	imes {10^{ - 2}}\,m$,and $B = B_H = 5 	imes {10^{ - 5}}\,T$.Equating the magnetic field of the coil to the horizontal component of Earth's magnetic field:$5 	imes {10^{ - 5}} = \frac{{4\pi 	imes {{10}^{ - 7}} 	imes i}}{{2 	imes 5 	imes {{10}^{ - 2}}}}$$5 	imes {10^{ - 5}} = \frac{{2\pi 	imes {{10}^{ - 7}} 	imes i}}{{5 	imes {{10}^{ - 2}}}}$$i = \frac{{5 	imes {{10}^{ - 5}} 	imes 5 	imes {{10}^{ - 2}}}}{{2 	imes 3.14 	imes {{10}^{ - 7}}}}$$i = \frac{{25 	imes {{10}^{ - 7}}}}{{6.28 	imes {{10}^{ - 7}}}} \approx 3.98\,A \approx 4\,A$.Therefore,the correct option is $B$.

What should be the current $i$ (in $A$) in a circular coil of radius $5\,cm$ to annul the horizontal component of Earth's magnetic field ${B_H} = 5 \times {10^{ - 5}}\,T$?

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