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Question: The magnetic flux of \(500\mu Wb\) passing through a 200 turn coil is reversed in\(20\times {{10}^{-...

The magnetic flux of 500μWb500\mu Wb passing through a 200 turn coil is reversed in20×10−320\times {{10}^{-3}} seconds. The average e.m.f. induced in the coil in volt is
A. 2.5
B. 5.0
C. 7.5
D. 10.0

Explanation

Solution

We are given the magnitude of magnetic flux in the question and we know that emf is only induced when there is a change in magnetic flux. Thus we could first find the change in flux due to its reversal. Then you could recall the expression for induced emf in terms of change in flux and substitute accordingly to get the answer.
Formula used:
Expression for emf,
ε=−nΔϕΔt\varepsilon =-n\dfrac{\Delta \phi }{\Delta t}

Complete answer:
In the question, we are given a magnetic flux of500μWb500\mu Wb that is passing through a coil of 200 turns. This flux is reversed in the time interval of 20×10−3s20\times {{10}^{-3}}s and we asked to find the average e.m.f. induced in the coil in volts. So,
n=200n=200 ……………………………………… (1)
ϕ1=500μWb{{\phi }_{1}}=500\mu Wb
As the flux is just reversed, the direction of the flux is only changed with the same magnitude,
ϕ2=−500μWb{{\phi }_{2}}=-500\mu Wb
So, change in flux is given by,
Δϕ=ϕ2−ϕ1\Delta \phi ={{\phi }_{2}}-{{\phi }_{1}}
Δϕ=(−500−500)μWb\Delta \phi =\left( -500-500 \right)\mu Wb
∴Δϕ=−1000×10−6Wb\therefore \Delta \phi =-1000\times {{10}^{-6}}Wb ……………………………………….. (2)
Time interval is given in the question as,
Δt=20×10−3s\Delta t=20\times {{10}^{-3}}s …………………………………………….. (3)
Now, let us recall the expression for average emf induced in a coil due to the change in flux,
ε=−nΔϕΔt\varepsilon =-n\dfrac{\Delta \phi }{\Delta t} …………………………………………….. (4)
Now, we could directly substitute (1), (2) and (3) in (4), we get,
ε=−200×−1000×10−620×10−3\varepsilon =-200\times \dfrac{-1000\times {{10}^{-6}}}{20\times {{10}^{-3}}}
∴ε=10V\therefore \varepsilon =10V
Therefore, we found the average e.m.f. induced in the coil in volt to be 10V.

Hence, option D is found to be the right answer.

Note:
You may have noticed the negative sign in the expression of induced emf. This negative sign represents the direction of current in a closed loop. Also, from the expression we see that the induced emf can be increased by increasing the number of turns in the coil as the induced emf is seen to be directly proportional to the number of turns.