A rectangular frame of wire `abcd` has dimensions `1mxx 0.5m` and a total resistance of `30Omega` . It is pulled out of a magnetic field `B=2T` by applying a force of `1N` . It is found that the frame moves with constant speed.
(i) The constant speed is `30m//sec`
(ii) The emf induced in loop is `30` volt
(iii) The p.d. between `a` and `b` is `25V`
(iv) The p.d. between `c` and `d` is `5V` .

Options

A. `(i), (ii), (iii)`
B. `(ii), (iii), (iv)`
C. `(i), (ii), (iii)`
D. all

Answer

D

Explanation

Induced emf `e=Bvl`
Induced current `i=(e)/(R)=(Bvl)/(R)`
Magnetic force `F=Bil=(B^(2)vl^(2))/(R)`
`1=((2)^(2)vxx(0.5)^(2))/(30)`
`1=30m//sec`
`e=Bvl=22xx30xx0.5=30V`
`i=e//R=30//30=1A`
`r=(30)/(2(1+0.5))xx0.5=5Omega`
`v_(b)-v_(a)=e-ir=30-1xx5=25V`
`V_(c)-V_(d)=ixx5=1xx5=5V` .