The earth's magnetic field at a given point is 0.5 × 10-5 Wb / m 2 . This field is to be annulled by magnetic induction at the center of a circular conducting loop of radius 5.0 cm . The curtent required to be flown in the loop is nearly

Question

The earth's magnetic field at a given point is 0.5 × 10-5 Wb / m 2 . This field is to be annulled by magnetic induction at the center of a circular conducting loop of radius 5.0 cm . The curtent required to be flown in the loop is nearly (A) 0.2 A (B) 0.4 A (C) 4 A (D) 40 A

Tardigrade Admin · Accepted Answer

The magnetic field at the centre of a circular loop carrying current

I

is given by

B = \frac{m _{0} I}{2 r}

where

r

is the radius of the circular loop. Given that

r = 5.0 c m = 0.05 m

.
Now,

B = \frac{μ _{0} I}{2 r} = 0.5 \times 1 0^{- 5}

\Rightarrow I = \frac{0.5 \times 1 0 ^{- 5} \times 2 \times 0.05}{μ _{0}}

= \frac{0.5 \times 1 0 ^{- 5} \times 0.1}{4 π \times 1 0 ^{- 7}}

= 0.3978 \approx 0.4 \overset{˚}{A}

.

Q. The earth's magnetic field at a given point is 0.5 ×10−5Wb/m2. This field is to be annulled by magnetic induction at the center of a circular conducting loop of radius 5.0cm. The curtent required to be flown in the loop is nearly

0.2 A

0.4 A

4 A

40 A

The magnetic field at the centre of a circular loop carrying current I is given by B=2rm0​I​ where r is the radius of the circular loop. Given that r=5.0cm=0.05m. Now, B=2rμ0​I​=0.5×10−5 ⇒I=μ0​0.5×10−5×2×0.05​ =4π×10−70.5×10−5×0.1​ =0.3978≈0.4A˚.

Q. The earth's magnetic field at a given point is $0.5$ $\times 1 0^{- 5} Wb / m^{2} .$ This field is to be annulled by magnetic induction at the center of a circular conducting loop of radius $5.0 c m .$ The curtent required to be flown in the loop is nearly