A metallic rod of ‘L’ length is rotated with angular frequency of ‘ $straight omega$ ’ with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius L, about an axis passing through the centre and perpendicular to the plane of the ring. A constant and uniform magnetic field B parallel to the axis is present everywhere. Deduce the expression for the emf between the centre and the metallic ring.

Solution

Emf is induced is given by, $epsilon space equals fraction numerator d phi subscript B over denominator d t end fraction equals straight d over dt left parenthesis BA right parenthesis straight space equals straight space straight B straight space dA over dt$
where, $dA over dt comma space$ is the rate of change of area of the loop formed by the sector OPQ.

At any instant of time t, let be the angle between the rod and the radius of the circle at P.
Area of the sector OPQ = $straight R squared cross times fraction numerator straight theta over denominator 2 straight pi end fraction equals 1 half straight R squared straight theta$ ;R is the radius of the circle.
Therefore, emf induced is, $Error converting from MathML to accessible text.$
$straight epsilon equals straight space 1 half BR squared dθ over dt equals BωR squared over 2$

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?