A square loop of wire consisting of a single turn is...

A square loop of wire consisting of a single turn is perpendicular to a uniform magnetic field. The square loop is then re-formed into a circular loop, which also consists of a single turn and is also perpendicular to the same magnetic field. The magnetic flux that passes through the square loop is 7.68 × 10-3 Wb. What is the flux that passes through the circular loop?

Transcript

00:01 Equation for the magnetic flex is given by phi is equal to b a cos theta here b is the magnitude of the magnetic field is the area of cross -section and theta is the angle between the magnetic field and the area vector it is given that the square loop is perpendicular to the magnetic field this implies the area vector must be parallel to the magnetic field oh the value of theta must be zero substituting the value of theta gives, 5 is equal to b a cos 0 degree, which is equal to b a.

00:35 The equation for the area of the square loop is given by a is equal to a square.

00:41 Here, small letter a is the side of the square loop.

00:44 Substituting this in the equation for the magnetic flux gives, 5 is equal to b a square.

00:51 It is given that the square loop is reformed into a circular loop.

00:56 When it was done, the circumference of the square lobe must be equal to the circumference of the circle.

01:03 The circumference of the square is equal to 4a and the circumference of the circle is equal to 2 pi r, where r is the radius of the circle.

01:13 Rearranging thus for the radius of the circular loop gives, r is equal to 4a by 2 pi, which is equal to 2a by pi.

01:23 The equation for the magnetic plus through the circular loop is given by 5 prime is equal to b, a, prime, cos theta, where a prime is the area of the circular loop.

01:36 It is given that the circular loop is also perpendicular to the magnetic field.

01:41 This implies the area vector must be parallel to the magnetic field, so that the value of theta will be 0 degree...

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