At the equator a 1000 turn coil with a cross sectional area of 300 cm2 and a resistance of 15 #Omega# is aligned with its plane perpendicular to the earth’s magnetic field of 7*10^-5 T . If the coil is flipped over how much charge flows through it?

Answer 1
Important information missing: Time taken to flip over the coil Let this be #=t#. However, we will see that it is not required for the final answer.
We know that the average induced current #I_(av)# in the coil is given by Faraday’s law of induction.
#I_(av)=varepsilon/R# .........(1) where #varepsilon# is the induced emf produced due to change in flux linked with the coil and #R# is the resistance of coil.

Lenz's law also tells us that the rate at which the magnetic flux associated with the coil shifts and opposes it is known as the induced emf in the coil.

#varepsilon=-(Deltaphi)/t# .......(2)
The coil of #N# turns of area #A# has flux #phi# linked with it when it is initially aligned with its plane perpendicular to the earth’s magnetic field #B#. As the coil is flipped over the linked flux becomes #-phi#. As such
#Deltaphi=-2phi=-2NBA# ......(3)

By rewriting (1) using (2) and (3) as support, we obtain

#I_(av)=(2NBA)/(Rt)# ......(4)
Now charge through coil in time #t# can be calculated from the definition of current.
#I=(Q)/t# #=>Q=It# ......(5)

By applying (4), we obtain

#Q=(2NBA)/(Rt)xxt# #=>Q=(2NBA)/(R)#

Putting specified values into SI units yields

#Q=(2xx1000xx(7xx10^-5)xx300/10^4)/15# #=>Q=2.8xx10^-4\ C#
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Answer 2

When the coil is aligned with its plane perpendicular to the Earth's magnetic field, no induced current is produced because the angle between the magnetic field and the normal to the coil's plane is 90 degrees.

When the coil is flipped over, the angle between the magnetic field and the normal to the coil's plane is still 90 degrees, so the change in flux is zero. Therefore, according to Faraday's law of electromagnetic induction, no induced electromotive force (emf) is generated, and thus, no charge flows through the coil.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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