Discuss special cases of Biot-Savart law.
$(1)$ If $\theta=0^{\circ}, \sin 0^{\circ}=0$, so that $d \mathrm{~B}=0$ i.e. the magnetic field is zero at points on the axis of the current element.
$(2)$ If $\theta=90^{\circ}, \sin 90^{\circ}=1$ so that $d \mathrm{~B}=$ is maximum. i.e. the magnetic field due to a current element is maximum in a plane passing through the element and perpendicular to its axis.
A cylindrical cavity of diameter a exists inside a cylinder of diameter $2$a shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density $J$ flows along the length. If the magnitude of the magnetic field at the point $P$ is given by $\frac{N}{12} \mu_0$ aJ, then the value of $N$ is :
An electron revolves around nucleus with rotational frequency $'f'$ in circular orbit, due to this magnetic induction produced at nucleus position is $'B'$ then radius of circular orbit is directly proportional to
Two concentric coils each of radius equal to $2\pi \,{\rm{ }}cm$ are placed at right angles to each other. $3$ $ampere$ and $4$ $ampere$ are the currents flowing in each coil respectively. The magnetic induction in $Weber/{m^2}$ at the centre of the coils will be $({\mu _0} = 4\pi \times {10^{ - 7}}\,Wb/A.m)$
A long straight wire, carrying current $I$ is bent at its mid-point to form an angle of $45^{\circ}$. Induction of magnetic field (in tesla) at point $P$, distant $R$ from point of bending is equal to
A straight wire of finite length carrying current $l$ subtends an angle of $60^{\circ}$ at point $P$ as shown. The magnetic field at $P$ is