Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Obtain an expression for the mutual inductance between a long straight wire and a square loop of side a as shown in Fig.

Q6.16 (a) Obtain an expression for the mutual inductance between a long straight wire and a square loop of side a as shown in Fig.            

Answers (1)

best_answer

Here let's take a small element dy in the loop at 'y' distance from the wire

Area of this element dy :

dA=a*dy

The magnetic field at dy (which is y distance away from the wire) is 

B=\frac{\mu _0I}{2\pi y}

The magnetic field associated with this element dy

d\phi =BdA

d\phi=\frac{\mu _0I}{2\pi y}*ady=\frac{\mu _0Ia}{2\pi}\frac{dy}{y}

\phi=\int_{x}^{a+x}\frac{\mu _0Ia}{2\pi}\frac{dy}{y}=\frac{\mu _0Ia}{2\pi}[lnx]^{a+x}_a=\frac{\mu _0Ia}{2\pi}ln[\frac{a+x}{x}]

Now As we know

\phi=MI where M is the mutual inductance 

So, 

\phi=MI=\frac{\mu _0Ia}{2\pi}ln[\frac{a+x}{x}]

M=\frac{\mu _0a}{2\pi}ln[\frac{a+x}{x}]

Hence mutual inductance between the wire and the loop is given by :

 \frac{\mu _0a}{2\pi}ln[\frac{a+x}{x}]

 

Posted by

Pankaj Sanodiya

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question