As shown in the above figure, a loop surrounds three regions of the magnetic field where the magnitude of the magnetic field is decreasing at a constant rate α . Take the area of each region as A . Now find the oint overset arrow E. overset arrow d l along the given loop, where overset arrow E is the induced electric field.

Question

<img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-mz5kahwjzyrhfbnm.jpg" /> As shown in the above figure, a loop surrounds three regions of the magnetic field where the magnitude of the magnetic field is decreasing at a constant rate α . Take the area of each region as A . Now find the oint overset arrow E. overset arrow d l along the given loop, where overset arrow E is the induced electric field. (A) α A  (B) -α A  (C) 3 α A  (D) -3α A

Tardigrade Admin · Accepted Answer

From faraday law of emf, a time varying magnetic field produces electric field according to the following equation:

\oint E \cdot d l = - \frac{d ϕ}{d t}

also,

ϕ = B . A

is the magnetic flux assosiated substituting this in the above equation,we get:

\Rightarrow \oint E \cdot d l = - \frac{d ( B \cdot A )}{d t}

\Rightarrow \oint E \cdot d l = - A \frac{d B}{d t}

Here it is given that

\frac{d B}{d t} = α

and now taking the sign of flux according to right hand curl rule we get:

\Rightarrow \oint E \cdot d l = - [- (- α A) - (- α A) + (- α A)]

\Rightarrow \oint E \cdot d l = - α A

$α A$

$- α A$

$3 α A$

$- 3 α A$

Q. As shown in the above figure, a loop surrounds three regions of the magnetic field where the magnitude of the magnetic field is decreasing at a constant rate α . Take the area of each region as A . Now find the ∮E→.dl→ along the given loop, where E→ is the induced electric field.

αA

−αA

3αA

−3αA

$α A$

$- α A$

$3 α A$

$- 3 α A$