List of top Physics Questions on Magnetic Field Due To A Current Element, Biot-Savart Law asked in JEE Main

The angle between vector \( \vec{Q} \) and the resultant of \( (2\vec{Q} + 2\vec{P}) \) and \( (2\vec{Q} - 2\vec{P}) \) is:

Two circular coils \(P\) and \(Q\) of \(100\) turns each have the same radius of \(\pi \, \text{cm}\). The currents in \(P\) and \(Q\) are \(1 \, \text{A}\) and \(2 \, \text{A}\) respectively. \(P\) and \(Q\) are placed with their planes mutually perpendicular with their centers coinciding. The resultant magnetic field induction at the center of the coils is \(\sqrt{x} \, \text{mT}\), where \(x =\) ______.
[Use \(\mu_0 = 4 \pi \times 10^{-7} \, \text{TmA}^{-1}\)]

As shown in the figure, a current of $2 A$ flowing in an equilateral triangle of side $4 \sqrt{3} cm$ The magnetic field at the centroid $O$ of the triangle is

 (Neglect the effect of earth's magnetic field)

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0.8 T. When released the radius of the loop starts shrinking at a constant rate of 2 cms^–1. The induced emf in the loop at an instant when the radius of the loop is 10 cm will be _____ mV.

A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from \(+ve\) z direction and lying in xy plane is shown in figure. The plot of \(\hat{j}\) component of magnetic field (By) at a distance ‘a’ (less than radius of the coil) and on yz plane vs z coordinate look like

Two identical wires $A$ and $B$, each of length $l$, carry the same current $I$. Wire $A$ is bent into a circle of radius $R$ and wire $B$ is bent to form a square of side $a$. If $B_A$ and $B_B$ are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\frac{B_A}{B_B}$ is :