DPP

A copper rod of mass $m$ rests on two horizontal rails distance$L$ apart and carries a current of $\mathrm{I}$ from one rail to another. The coefficient of static friction between the rod and the rail is ${\mu }_s$. What is the angle (relative to the vertical) of the smallest magnetic field that puts the rod on the verge of sliding?

A parabolic wire, as shown in the figure, is located in $xy$ plane and carries a current $I=10 \mathrm{A}$. A uniform magnetic field of intensity, $2\sqrt{2} \mathrm{T}$ making an angle of $45°$ with $x$-axis exists throughout the plane. If the coordinates of the endpoint $P$ of wire are $(2 \mathrm{m},1.5 \mathrm{m})$, then the total force acting on the wire is:

The figure shows an equilateral triangle $ABC$ of side $l$ carrying currents, placed in uniform magnetic field $B$. The magnitude of magnetic force acting on the triangle is:

A horizontal metallic rod of a mass $m$ and length $l$ is supported by two identical vertical springs of spring constant $K$ each and natural length $l_0$. A current $i$ is flowing in the rod in the direction shown. If the rod is in equilibrium, then the length of each spring in this state is given as:

In the figure given, a current $I_1$ is established in the long straight wire $AB$. Another wire $CD$, carrying current $I_2$ is placed in the plane of the paper. The line joining the ends of the wire $CD$ is perpendicular to the wire $AB$. The resultant force on the wire $CD$ is:

$ABCDE$ is a very long wire carrying current $i_1$ as shown. The portion $BCD$ is a semicircle with centre at $O$. Another very long wire passes through point $O$, perpendicular to the plane of $ABCDE$ and it carries current $i_2$ outside the plane of paper. The two wires,

In the given figure, an infinitely long wire, at $E$, is kept perpendicular to the paper, carrying current inwards. Which of the following statements is correct?

A current-carrying conductor is in the form of a sine curve as shown, which carries current $I$. If the equation of this curve is $y=2\sin \left(\frac{\pi x}{L}\right)$ and a uniform magnetic field exists in space, then,