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A tangent galvanometer has a coil with 50 turns and radius equal to 4 cm. A current of 0.1 A is passing through it. The plane of the coil is set parallel to the earth’s magnetic meridian. If the value of the earth’s horizontal component of the magnetic field is 7×105Tesla andμ0=4π×107WbA1m1, the deflection in the galvanometer needle will be:
A45B. 48.3  C. 50.7  D52.7

Answer
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Hint: We have to find deflection of galvanometer needle when current is given for the tangent galvanometer. By using formula for the tangent galvanometer we can find the deflection of the galvanometer needle. The permeability in free space is also given. Further, we can discuss briefly about the tangent galvanometer.

Formula used:
I=2rBHtanθμ0n

Complete answer:
Tangent galvanometer is used to measure electric current with the help of a compass needle. It basically compares the magnetic field produced by an unknown electric current with the earth’s magnetic field. Its name is given on the basis of its operation as works by the tangent law of magnetism. The magnetic field of the coil is given by
B=μ0nI2r
Where n is number of turns, I is the current flowing through the coil, r is the radius of the coil and μ0is the permeability in free space.
From, the tangent law
B=BHtanθ
Where BH is the earth’s horizontal component of the magnetic field. By substituting the value of B in the above tangent law we can field the current passing through coil. Hence current for the tangent galvanometer is given as
I=2rBHtanθμ0n
Here we have to find deflection in the galvanometer needle which is given as
θ=tan1(Iμ0n2rBH)
Given values are I=0.1A,n=50,r=4cm,BH=7×105Tesla,μ0=4π×107WbA1m1
Substituting all value in the above equation we get
θ=tan1((0.1)×4π×107×502×4×102×7×105)
Substituting π=3.14
θ=tan1((0.1)×4×3.14×107×502×4×102×7×105)θ=tan1(62.8×10756×107)θ=tan1(1.121)θ=48.2648.3  
So the angle made by the galvanometer needle is 48.3  .

So, the correct answer is “Option B”.

Note:
While calculating, always make sure that all units are the same, if not change it. Like, here the radius was given in centimetre, while substituting we changed its unit in meters. If the unit was not changed we would have got the wrong answer. These are the very small things where we can make mistakes.
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