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Question: The earth's magnetic field at a given point is\(0.5 \times {10^{ - 5}}Wb - {m^{ - 2}}\). This field ...

The earth's magnetic field at a given point is0.5×10−5Wb−m−20.5 \times {10^{ - 5}}Wb - {m^{ - 2}}. This field is to be annulled by magnetic induction at the center of a circular conducting loop of the radius5.0cm5.0cm. The current required to be flown in the loop is near-
(a)\left( a \right) 0.2A0.2A
(b)\left( b \right) 0.4A0.4A
(c)\left( c \right) 4A4A
(d)\left( d \right) 40A40A

Explanation

Solution

Hint So this question is based on the concept of magnetic induction or magnetic field. Since by using the formula for the magnetic induction which isB=μnI/2rB = \mu nI/2r. So from this, we will be able to find the required current to fly in the loop.
Formula used:
Magnetic induction at the center of circular conducting loop,
B=μnI/2rB = \mu nI/2r
Here,
BB, will be the magnetic field
nn, will be the number of turns
II, will be the current
rr, will be the radius

Complete Step By Step Solution So first of all let assume a loop having the radius 5cm5cmand is carrying the current II.
So from the formula which we have already known above, magnetic induction will be
B=μnI/2rB = \mu nI/2r
Therefore, first of all, we will see the values which we have,
n=1n = 1
r=5cm=0.05mr = 5cm = 0.05m , And
μ=4π×10−7\mu = 4\pi \times {10^{ - 7}}
Here the magnetic field of the earth at that point will due to the conducting loop
So it will be
B=0.5×10−5Wb/sq.mB = 0.5 \times {10^{ - 5}}Wb/sq.m
Now we have to calculate the current so the formula will be
i=2rB/μi = 2rB/\mu
Putting the values, we get
⇒i=0.5×10−5×10×10−24π×10−7\Rightarrow i = \dfrac{{0.5 \times {{10}^{ - 5}} \times 10 \times {{10}^{ - 2}}}}{{4\pi \times {{10}^{ - 7}}}}
Now on solving the above equation, we get
⇒i=54π\Rightarrow i = \dfrac{5}{{4\pi }}
And it will be written as
⇒i=3588\Rightarrow i = \dfrac{{35}}{{88}}
And on solving the above line, we get
∴i=0.3980A=0.4A\therefore i = 0.3980A = 0.4A
So, 0.4A0.4Aof the required current to flow in the loop.

Therefore, the option BB will be correct.

Note In an attractive circuit, magnetic inductance is a similarity to inductance in an electrical circuit. This model makes magneto thought process power the simple of electromotive power in electrical circuits and time pace of progress of magnetic flux, the simple of electric flow. When there is a magnetic field that is variable in time that will make an initiated electric field and this we will call it magnetic induction.