Question

# A long straight current-carrying wire passes normally through the center of the circular loop if the current through the wire increases. Will there be an induced emf in the loop? Justify?

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Solution

## Step 1: Given data and figureGiven information - A long straight current-carrying wireCircular loop connected to the wireThe magnetic field on the loop The magnetic field on the loop is given by the right-hand thumb rule in which the thumb represents the direction of the current and the curl of the fingers represents the direction of the magnetic field.The diagrammatical representation of their given case is,Step 2: Formula UsedMagnetic flux is given by, $\varphi =BA\mathrm{cos}\theta$, where $B$ is the magnetic field, $A$ is the area, and $\theta$ is the angle between area vector and magnetic fieldStep 3: SolutionFrom the figure, we can understand the angle between the area vector and the magnetic field so, it is considered 90 degrees.As induced e.m.f directly proportional to the rate of change of magnetic flux $\left({\Phi }_{B}\right)$${\Phi }_{B}=B.A=BA\mathrm{cos}\theta \phantom{\rule{0ex}{0ex}}B\perp A\phantom{\rule{0ex}{0ex}}{\Phi }_{B}=BA\mathrm{cos}90°=0$So, induced EMF will be $0$.No, there will not be an induced emf occurring in the loop as magnetic flux does not change linked with the circular loop. Because magnetic field lines are parallel to the plane of the loop.

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