"On flowing current in a conducting wire, a magnetic field is produced around it." This is a law of

$A$ toroidal solenoid with air core has an average radius $R$,number of turns $N$,and area of cross-section $A$. The self-inductance of the solenoid is (Neglect the field variation across the cross-section of the toroid).

$A$ solenoid of length $50 \,cm$ having $100$ turns carries a current of $2.5 \,A$. The magnetic field at one end of the solenoid is

Two wires carrying currents of $5 \ A$ and $2 \ A$ are enclosed in a circular loop as shown in the figure. Another wire carrying a current of $3 \ A$ is situated outside the loop. The value of $\oint \overrightarrow{B} \cdot d\overrightarrow{l}$ around the loop is ($\mu_0 = \text{permeability of free space}$,$d\overrightarrow{l}$ is the length element of the Amperian loop).

In a toroid,the magnetic field on the axis is to be calculated given the radius $r = 0.5 \, cm$,current $I = 1.5 \, A$,number of turns $N = 250$,and relative permeability $\mu_r = 700$. Find the magnetic field $B$ (in Tesla). (in $.5$)

$A$ coil wrapped around a toroid has an inner radius of $20 \,cm$ and an outer radius of $25 \,cm$. If the wire wrapping makes $800$ turns and carries a current of $12 \,A$, the maximum and minimum values of the magnetic field within the toroid are: