27

A solenoid wound  over a rectangular frame if all the linear dimensions of the frame are increased by factor of 3 and no of turns per unit lenght remains same the self inductance is

Hello Sagar,

Please do not post unneccessary posts here and there. 

Is the answer 63? Here is what I found. Here ~ means proportional

For a rectangular frame 

L~l. b. h of the frame

Initially let length was l1

After it is increased by 3 factors i.e 3l new length l2=3l+l=4l

Similarly b1=b, b2=4b and

h1=h, h2=4h

So L1~l1. b1. h1

And L2~l2. b2. h2

Taking ratio

L1/L2=(l1. b1. h1)/(l2. b2. h2)

Put their respective values we get

L1/L2=1/(4.4.4)

L2=64L1

Now to find the increase we have to subtract. Let both L1 and L2 be=L

Now since L2=64L1

Therefore factor increase=64L-L=63

63

Since L= Mo n2 volume

      L1/l2= l b h / L B H=1/3×3×3 

    And is l1 = 1/27 l2 

      = L2 =27l1

my answer is 27 but  a simiar question has come in jee main 2019  11 jan 

and they have given answer 3

Answer is 3

Use N²uA/l=L

A is area and l is length of box

63