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Question: Earth’s magnetic induction at a certain point is 7 x \({10^{-5\;}}\)Wb/\({m^2}\). This field is to b...

Earth’s magnetic induction at a certain point is 7 x 10−5  {10^{-5\;}}Wb/m2{m^2}. This field is to be annulled by the magnetic induction at the centre of a circular conducting loop 15.0 cm in radius. The required current present in the loops is
(a) 0.56 A.
(b) 16.7 A.
(c) 0.28 A.
(d) 2.8 A.

Explanation

Solution

Hint
The term annulled might make it confusing. This term only means that the magnetic field of a ring must be equated to earth’s magnetic field. Then the formula B=μ  ∘I2rB = \dfrac{{\mu {\;_ \circ }I}}{{2r}} can be applied to solve the question.

Complete step by step answer
The magnetic field at the centre of a ring having radius is given by the formula,
B=μ  ∘I2rB = \dfrac{{\mu {\;_ \circ }I}}{{2r}}
where B is the magnetic field present in the loop.
I is the current passing in the circumference of the loop.
R is the radius of the cross section area of the loop.
Putting the given values in the equation we have,
⇒7×10−5=4π×10−72×15×10−2I\Rightarrow 7 \times {10^{ - 5}} = \dfrac{{4\pi \times {{10}^{ - 7}}}}{{2 \times 15 \times {{10}^{ - 2}}}}I
⇒I=210×10−74π×10−7\Rightarrow I = \dfrac{{210 \times {{10}^{ - 7}}}}{{4\pi \times {{10}^{ - 7}}}}
⇒I=16.71A\Rightarrow I = 16.71A
Hence the current in the circuit is 16.71 A which does not match with any of the given options.

Note
At times this kind of question may contain both vertical and horizontal magnetic fields and their resultant. In those questions we only have to take either horizontal or vertical magnetic fields by seeing the sense of the magnetic field.