Question

The earth's magnetic field at a given point is $0.5\times {10}^{-5}Wb{m}^{-2}$. This field is to be annulled by magnetic induction at the centre of a circular conducting loop of radius $5.0$cm. The current required to be flown in the loop is nearly

• A. $0.2A$
• B. $0.4A$
• C. $4A$
• D. $40A$

Answer 1

Answer: (B)

$0.4A$

Fields created at the centre $=0.5\times {10}^{-5}Wb/m^2$

Due to current in circular loop, field created in the centre $=\frac{{\mu }_{0}i}{2r}$

$=\frac{4\pi \times {10}^{-7}\times i}{2\times 5\times {10}^{-2}}=0.5\times {10}^{-5}$

$i=\frac{0.5\times {10}^{-5}\times 10\times {10}^{-2}}{4\pi \times {10}^{-7}}=\frac{5}{4\pi }=\frac{35}{88}$

$=0.3980=0.4A$