Magnetic potential energy:
When a current carrying loop is placed in an external magnetic field the torque is acted upon the current loop which tends to rotate the current loop in a magnetic field. Therefore the work is done to change the orientation of the current loop against the torque. This work is stored in the form of magnetic potential energy in the current loop. This is known as the magnetic potential energy of the current loop.
Note: The current loop has magnetic potential energy depending upon its orientation in the magnetic field.
Derivation of Potential energy of current-loop in a magnetic field:
Let us consider, A current loop of magnetic moment $\overrightarrow{m}$ is held with its axis at an angle $\theta$ with the direction of a uniform magnetic field $\overrightarrow{B}$. The magnitude of the torque acting on the current loop or magnetic dipole is
$\tau=m \: B \: sin\theta \qquad(1)$
Now, the current loop is rotated through an infinitesimally small angle $d\theta$ against the torque. The work done to rotate the current loop
$dW=\tau \: d\theta$
$dW=m \: B \: sin\theta \: d\theta $ {from equation $(1)$}
If the current loop is rotated from an angle (or orientation) $\theta_{1}$ to $\theta_{2}$ then the work done
$W=\int_{\theta_{1}}^{\theta_{2}} m \: B \: sin\theta d\theta$
$W= m \: B \: \left[ -cos\theta \right]_{\theta_{1}}^{\theta_{2}} $
$W= m \: B \: \left( cos\theta_{1} - cos\theta_{2} \right) $
This work is stored in the form of potential energy $U$ of the current loop :
$U= m \: B \: \left( cos\theta_{1} - cos\theta_{2} \right) $
If $\theta_{1}=90^{\circ}$ and $\theta_{2}= \theta$
$U= m \: B \: \left( cos90^{\circ} - cos\theta \right) $
$U= - m \: B \: cos\theta $
$U= - \overrightarrow{m} . \overrightarrow{B}$
Thus, a current loop has minimum potential energy when $\overrightarrow{m}$ and $\overrightarrow{B}$ are parallel and maximum potential energy when $\overrightarrow{m}$ and $\overrightarrow{B}$ are antiparallel.
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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