MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12
        A long horizontal wire AB, which is free to move in a vertical plane and carries a steady current of 20A, is in equilibrium at a height of 0.01m over another parallel wire CD which is fixed in a horizontal plane. Show that AB is slightly depressed , it executes simle harmonic motion. Find the period of oscillations. 
10 years ago

Answers : (1)

askIITianexpert IITDelhi
8 Points
							

Weight per unit length of wire is balanced by magnetic force per unit length.

or, { 4¶*10-7*i1*i2 }/d2 = mg/l       where i=   Current through wire CD

                                                                      i=    Current through wire AB     =   20A

                                                                      d=      Vertical separation between wires   = 0.01 mtrs.

Let wire AB is depressed by 'x' then,

                                                               Vertical separation between wires = d-x

Now magnetic force per unit length on AB =   { 4¶*10-7*i1*i2 }/(d-x)2 = K/(d-x)2   where K is a constant equal to  4¶*10-7*i1*i2.

or,   Net vertical force per unit length on AB =[  { 4¶*10-7*i1*i2 }/(d-x)2 ] - (mg/l) = K [1/ (d-x)2 - 1/d2 ]

                                                                             =  K [( 2dx-x2 )/{ (d-x)2 *d2 } ]  

Taking x/d=µ  &  x<<d;i.e. µ<<1

Simplifying above expression give R.H.S.  =  2dx/d4 [(1-µ/2)/{(1-µ)2}]K = 2x/d3 K        : Ignoring the negligible terms 1-µ & 1-µ/2 equal to 1.

L.H.S  = (m/l)w2x = 2x/d*( K/d2 )   ; or,    w2 = 2g/d          where w=angular frequency of SHM with F=constant*x(Hookes' Law)

                                                                                                   K/d2 = mg/l

So,period = 2¶/w= ( 2¶ ) / [ (2g/d)1/2 ] = 0.14 sec.

 

10 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 110 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details