The mutual inductance between the rectangular | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The magnetic field $B$ at a distance $x$ from the long straight wire carrying current $i$ is given by $B = \frac{\mu_0 i}{2\pi x}$.Consider a smal

Vedclass · Accepted Answer

$M = \frac{\mu_0 a}{2\pi} \ln \left( 1 + \frac{b}{c} \right)$

Vedclass · Answer

(B) The magnetic field $B$ at a distance $x$ from the long straight wire carrying current $i$ is given by $B = \frac{\mu_0 i}{2\pi x}$.Consider a small rectangular strip of width $dx$ at a distance $x$ from the wire. The area of this strip is $dA = a \cdot dx$.The magnetic flux $d\phi$ through this strip is $d\phi = B \cdot dA = \left( \frac{\mu_0 i}{2\pi x} \right) a \cdot dx$.To find the total flux $\phi$ through the loop,we integrate from $x = c$ to $x = c + b$:$\phi = \int_{c}^{c+b} \frac{\mu_0 i a}{2\pi x} dx = \frac{\mu_0 i a}{2\pi} [\ln x]_{c}^{c+b} = \frac{\mu_0 i a}{2\pi} \ln \left( \frac{c+b}{c} \right) = \frac{\mu_0 i a}{2\pi} \ln \left( 1 + \frac{b}{c} \right)$.Since $\phi = M i$,the mutual inductance is $M = \frac{\mu_0 a}{2\pi} \ln \left( 1 + \frac{b}{c} \right)$.

The mutual inductance between the rectangular loop and the long straight wire as shown in the figure is $M$.

Similar Questions

Two coils $A$ and $B$ have a coefficient of mutual inductance $M = 2 \ H$. The magnetic flux passing through coil $A$ changes by $4 \ Wb$ in $10 \ s$ due to the change in current in coil $B$. Then:

$A$ small square loop of wire of side $l$ is placed inside a large square loop of wire of side $(L > l)$. The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to

The device that does not work on the principle of mutual induction is

$A$ solenoid of length $0.30 \, m$ has $2000$ turns. The area of its cross-section is $1.2 \times 10^{-3} \, m^2$. Around its central section,a coil of $300$ turns is wound. If an initial current of $2 \, A$ in the solenoid is reversed in $0.25 \, s$,then the $e.m.f.$ induced in the coil is:

What is the mutual inductance of a two-loop system as shown with centre separation $l$ where $l >> a$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module