Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard
  1. Home
  2. School
  3. (a) Define mutual inductance and write its S.I. unit. (b) A square loop of side ‘a’ carrying a current  is kept at distance x from an infinitely lo
# School

(a) Define mutual inductance and write its S.I. unit.
(b) A square loop of side ‘a’ carrying a current I_{2} is kept at distance x from an infinitely long straight wire carrying a current I_{1} as shown in the figure. Obtain the expression for the resultant force acting on the loop.

 
 
 
 
 

Answers (1)
S Safeer PP

(a) The property of two coils that opposes the change in current in one coil is defined as mutual Inductance. Let, the two coils :- coil 1 with number of turns N_{1} and coil 2 with the number of turns N_{2}.

The magnetic flux across them is \phi _{1} and \phi _{2} respectively.

Let I_{1} be the current through coil 1 and I_{2} be the current through coil 2.

Then, the mutual inductance (m) is given by:

M=\frac{N_{1}\phi _{1}}{I_{2}}=\frac{N_{2}\phi _{2}}{I_{2}}

The SI unit is Henry(H).

 

(b) Consider that two straight infinite parallel conducting wires with current I_{1} and I_{2} are separated by a distance x', then force per unit length of each wire is given by ;

F=\frac{\mu _{o}I_{1}I_{2}}{2\pi x} where, \mu _{o} is the magnetic permeability of free space.

such that, when the wires carry currents in the opposite direction, they repel and when the wires carry currents in the same direction, they attract.

Such that, F_{1}  and F_{2} must be equal. So, they can cancel out.

Now,

\frac{F_{3}}{a}=-\frac{\mu _{o}I_{1}I_{2}}{2\pi (x+a)}

\frac{F_{4}}{a}=\frac{\mu _{o}I_{1}I_{2}}{2\pi x}

Hence, the total force acting on the loop will be -

F = F_{3}+F_{4}

F=\frac{-\mu _{o}I_{1}I_{2}}{2\pi (x+a)}a+\frac{\mu _{o}I_{1}I_{2}}{2\pi x}a

F=\frac{\mu _{o}I_{1}I_{2}a}{2\pi}\left ( \frac{1}{x}-\frac{1}{x+a} \right )

F=\frac{\mu _{o}I_{1}I_{2}a^{2}}{2\pi x (x+a)}

Similar Questions

Latest Asked Questions

Most Viewed Questions

Related Chapters

Preparation Products

Knockout CUET (Physics, Chemistry and Mathematics)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout CUET (Physics, Chemistry and Biology)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Expert Mentorship, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Expert Mentorship, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Expert Mentorship, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
Start Now
 
Exams
Articles
Questions