Question

A conducting rod AB of length l is projected on a frictionless frame PSRQ with velocity v0 at any instant. The velocity of the rod after time t is​

Answer 1

Answer:

If it's fully Frictionless then it will be v < vo

If it's somehow less frictionless then somewhat friction will act upon it, so it will be v > vo

Answer 2

Given:

A conducting rod AB of length l is projected on a frictionless frame PSRQ with velocity v0 at any instant.

To find:

Velocity after time t

Diagram:

$\boxed{\setlength{\unitlength}{1cm}\begin{picture}(6,5)\thicklines\put(3,3){\line(0,-1){2}}\put(3,2){\vector(1,0){1}}\put(3,2){\vector(-1,0){0.75}}\put(4.25,2){ \vec{v}_{0} }\put(2,2){ \vec{a} }\put(2.95,3.25){A}\put(2.95,0.70){B}\end{picture}}$

Calculation:

Due to movement of rod , the EMF generated

$\therefore \: E = Blv_{0}$

Now , current through the rod AB having resistance r;

$\therefore \:i = \dfrac{ E}{r} = \dfrac{Blv_{0} }{r}$

So, magnetic force experienced by rod be F;

$\therefore \:F = i \times l \times B$

$= > \:F= \dfrac{{B}^{2} {l}^{2} v_{0} }{r}$

$= > \:a= \dfrac{{B}^{2} {l}^{2} v_{0} }{mr}$

This acceleration is opposite to the direction of the initial velocity.

So, after time t;

$\therefore \: v = v_{0} - at$

$= > \: v < v_{0}$

So, final answer is:

$\boxed{ \bf{ \: v < v_{0} }}$