In the figure,find out the magnetic field at the center $B$ (Given $I = 2.5 \; A, r = 5 \; cm$).

$A$ horizontal overhead power line carries a current of $90 \;A$ in east to west direction. What is the magnitude and direction of the magnetic field due to the current $1.5 \;m$ below the line?

$A$ long straight rod of diameter $4 \text{ mm}$ carries a steady current '$i$'. The current is uniformly distributed across its cross-section. The ratio of the magnetic fields at distances $1 \text{ mm}$ and $4 \text{ mm}$ from the axis of the rod is

Two infinitely long straight wires lie in the $xy$-plane along the lines $x=+R$ and $x=-R$. The wire located at $x=+R$ carries a constant current $I_1$ and the wire located at $x=-R$ carries a constant current $I_2$. A circular loop of radius $R$ is suspended with its centre at $(0,0, \sqrt{3} R)$ and in a plane parallel to the $xy$-plane. This loop carries a constant current $I$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $+\hat{j}$ direction. Which of the following statements regarding the magnetic field $\vec{B}$ is (are) true?
$(A)$ If $I_1=I_2$, then $\vec{B}$ cannot be equal to zero at the origin $(0,0,0)$.
$(B)$ If $I_1 > 0$ and $I_2 < 0$, then $\vec{B}$ can be equal to zero at the origin $(0,0,0)$.
$(C)$ If $I_1 < 0$ and $I_2 > 0$, then $\vec{B}$ can be equal to zero at the origin $(0,0,0)$.
$(D)$ If $I_1=I_2$, then the $z$-component of the magnetic field at the centre of the loop is $\left(-\frac{\mu_0 I}{2 R}\right)$.

Two long straight wires,each carrying a current $I$ in opposite directions,are separated by a distance $R$. The magnetic induction at a point midway between the wires is

$A$ coil having $100$ turns is wound tightly in the form of a spiral with inner and outer radii $1 \text{ cm}$ and $2 \text{ cm}$,respectively. When a current $1 \text{ A}$ passes through the coil,the magnetic field at the centre of the coil is