A rectanguar frame of wire abcd has dimensions `32cm xx 8.0 cm` and a total resistance of `2.0 Omega`. It is pulled out of a magentic field `B = 0.020 T` by applying a force of `3.2 xx10^(-5)` N . It is found that the frame moves with constant speed. Find (a) this constant speed, (b) the emf induced in the loop, (c) the potential difference between the points c and d.

Explanation

Refer to the previous problem
Net emf: `e=Bvl`
Indujced current `I=(e)/(R)=(Bvl)/(R)` , clockwise
Magnetic force on loop `F_(m)=Bll=(B^(2)vl^(2))/(R)` , towards left
Resistance of loop `R=2Omega`
. (a)`F=F_(m)=(B^(2)vl^(2))/(R)`
`3.2xx10^(-5)=((20xx10^(-3))^(2)v(0.08)^(2))/2`
`v=(2xx3.2xx10^(-5))/(4xx10^(-4)xx64xx10^(-4)=25m//sec`
`e=Bvl=20xx10^(-3)xx25xx0.08=0.04V`
Total length of loop `=2(32+8)=80cm`
Total resistance `=2Omega`
Resistance per unit lenght `=(2)/(80)=(1)/(4)Omega//cm`
Resistance of side `ab` and `cd=(1)/(40)xx8=(1)/(5)Omega`
Resistance of side `bc` and `ad(1)/(40)xx32=(4)/(5)Omega`
`I=(Bvl)/(R)=(20xx10^(-3)xx25xx0.08)/(2)=0.02`
`V_(b)-V_(a)=e-Ixx(1)/(5)=0.04-0.02xx0.2=0.036V`
`V_(c)-V_(d)=Ixx(1)/(5)`
`=0.02xx0.2=0.004V`