Question

Figure shows a horizontal magnetic field which is uniform above the dotted line and is zero below it. A long, rectangular, conducting loop of width L, mass m and resistance R is placed partly above and partly below the dotted line with the lower edge parallel to it. with what velocity should it be pushed downwards so that it may continue to fall without any acceleration,

Answer 1

Hint:It is given that it is a horizontal magnetic field. That it exists as dotted lines and its value is 0. There is a rectangular bar length of L, resistance of R is placed partly above and below the dotted line. It is pushed with a particular velocity and it falls without any acceleration.

Complete step by step answer:
Electromagnetic or magnetic induction is the production of an electromotive force across an electrical conductor in a changing magnetic field. A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents and magnetic materials.In this case, magnetic force is upwards and mg is downwards.
$e = Blv$
$\Rightarrow i = \dfrac{e}{R} = \dfrac{{Blv}}{R}$
We know that,
$F = iBl$
Substitute for i
$F = \dfrac{{Blv}}{R} \times Bl$
Therefore,
$F = \dfrac{{{B^2}{l^2}v}}{R}$
For uniform motion without any acceleration,
$mg = F$
$\Rightarrow mg = \dfrac{{{B^2}{l^2}v}}{R}$
Rearranging and finding the value of v. We get,
$v = \dfrac{{mgR}}{{{B^2}{l^2}}}$
With $v = \dfrac{{mgR}}{{{B^2}{l^2}}}$ the body will move without acceleration.

Additional information:In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A changing magnetic field, such as a magnet moving through a conducting coil, generates an electric field (and therefore tends to drive a current in such a coil). This is known as Faraday's law and forms the basis of many electrical generators and electric motors

Note:When the current is flowing through a conductor it produces a magnetic field here the cross (X) mark represents that the direction of magnetic field is outwards from the field and whereas the (.) mark represents that the direction of magnetic field is inwards to the field. This is a problem of electromagnetic induction. Students should be thorough with the topic . Proper understanding of the question is required to solve the problem. Also, proper implementation of the related formulas in the proper units is very essential too.Therefore, all the related formulas must be known for the correct answer of the problems.