Ampere's Circuital Law Statement:
When the current flows in any infinite long straight conductor then the line integration of the magnetic field around the current-carrying conductor is always equal to the $\mu_{0}$ times of the current.
$\int \overrightarrow{B}. \overrightarrow{dl} = \mu_{\circ} i$
Derivation of Ampere's Circuital Law:
Let us consider, An infinite long straight conductor in which $i$ current is flowing, then the magnetic field at distance $a$ around the straight current carrying conductor
$B=\frac{\mu_{\circ}}{2 \pi} \frac{i}{a}$
Now the line integral of the magnetic field $B$ in a closed loop is
$\oint \overrightarrow{B}. \overrightarrow{dl} = \oint \frac{\mu_{\circ}}{2 \pi} \frac{i}{a} dl$
$\oint \overrightarrow{B}. \overrightarrow{dl} = \frac{\mu_{\circ}}{2 \pi} \frac{i}{a} \oint dl$
$\oint \overrightarrow{B}. \overrightarrow{dl} = \frac{\mu_{\circ}}{2 \pi} \frac{i}{a} \left(2 \pi a \right) \qquad \left( \because \oint dl= 2 \pi a \right)$
$\oint \overrightarrow{B}. \overrightarrow{dl} = \mu_{\circ}i$
Modified Ampere's circuital law:
When the capacitor is placed in between the conductors then a current flows in the capacitor which is known as displacement current $\left(i_{d} \right)$. So modified Ampere's circuital law:
$\oint \overrightarrow{B}. \overrightarrow{dl} = \mu_{\circ} \left( i + i_{d} \right)$
Angle of Acceptance → If incident angle of light on the core for which the incident angle on the core-cladding interface equals the critical angle then incident angle of light on the core is called the "Angle of Acceptance. Transmission of light when the incident angle is equal to the acceptance angle If the incident angle is greater than the acceptance angle i.e. $\theta_{i}>\theta_{0}$ then the angle of incidence on the core-cladding interface will be less than the critical angle due to which part of the incident light is transmitted into cladding as shown in the figure below Transmission of light when the incident angle is greater than the acceptance angle If the incident angle is less than the acceptance angle i.e. $\theta_{i}<\theta_{0}$ then the angle of incidence on the core-cladding interface will be greater than the critical angle for which total internal reflection takes place inside the core. As shown in the figure below Transmission of lig
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