Magnetic Force on a Current Wire in Magnetic Field

An infinite wire placed along $z$-axis, has current $I_1$ in positive $z$-direction. A conducting rod placed in $xy$ plane parallel to y-axis has current $I_2$ in positive y-direction. The ends of the rod subtend angles of $+30°$ and $-60°$ at the origin with positive $x$-direction. The rod is at a distance $a$ from the origin. Find net force on the rod.

A $U$ shaped wire of mass $m$ and length $l$ is immersed with its two ends in mercury (see figure). The wire is in a homogeneous field of magnetic induction $B$. If a charge, that is, a current pulse $q=\int i\mathrm{d}t,$sent through the wire, the wire will jump up. Calculate, from the height $h$ that the wire reaches, the size of the charge or current pulse, assuming that the time of the current pulse is very small in comparison with the time of flight. Make use of the fact that impulse of force equals $\int F\mathrm{d}t,$ which equals $mv$. Evaluate $q$ for following details:
$B=0.1 \mathrm{Wb} {\mathrm{m}}^{-2}\mathrm{,} m=10 \mathrm{g}\mathrm{,}l=20 \mathrm{cm}$
$\text{\&} \mathit{h}=3 \mathrm{m}.\left[g=\mathrm{10} \mathrm{m} {\mathrm{s}}^{-2}\right]$

A rectangular loop of wire is oriented with the left corner at the origin, one edge along X-axis and the other edge along Y-axis as shown figure. A magnetic field is into the page and has a magnitude that is given by b=$\alpha \text{y}\text{where}\alpha \text{is }$constant. Find the total magnetic force on the loop if it carries current i.

Electric charge $q$ is uniformly distributed over a rod of length $l$. The rod is placed parallel to a long wire carrying a current $i$. The separation between the rod and the wire is $a$. Find the force needed to move the rod along its length with a uniform velocity $v$.

Figure shows a rectangular current-carrying loop placed $2 cm$ away from a long, straight, current-carrying conductor. What is the magnitude of the net force acting on the loop in ${10}^{-4}N$.

A positive charge is moving towards south in a space where magnetic field is pointing in the north direction. The moving charge will experience:

A wire carrying a current $I$ along the positive x-axis has length $L$. It is kept in a magnetic field $\overrightarrow{B}=\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-4\hat{\mathrm{k}} \right) \mathrm{T}$. The magnitude of the magnetic force acting on the wire is:

If two parallel current carrying wires $A\left(200 \mathrm{mA}\right)$ and $B\left(300 \mathrm{mA}\right)$ are separated by a distance of $1 \mathrm{cm}$, the force per unit length with each other is $\left({\mu }_0=4\pi \times {10}^{-7}\right)$

A wire of mass $100 \mathrm{g}$ carrying a current of $2 \mathrm{A}$ towards increasing $x$ is in the form of $y=x^2\left(-2 \mathrm{m}\le \mathrm{x}\le +2 \mathrm{m}\right)$. This wire is placed in a magnetic field $B=-0.02\hat{k}$ Tesla and gravity free region. The acceleration of the wire (in $\mathrm{m} {\mathrm{s}}^{-2}$) is:

The given figure shows an inductor and resistance fixed on a conducting wire. A movable conducting wire $PQ$ starts moving on the fixed rails from $t=0$ with constant velocity $1 \mathrm{m} {\mathrm{s}}^{-1}$. The work done by the external force on the wire $PQ$ in $2$ seconds is

Calculate the net force acting on wire element $\mathrm{BCD}$ due to the $2\mathrm{A}$ current.

The horizontal component of the earth's magnetic field at a certain place is $3.0\times {10}^{-5} \mathrm{T}$ and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of $2 \mathrm{A}$. What is the force per unit length on it when it is placed on a horizontal table and the direction of the current is east to west?

A thin uniform rod of negligible mass and length is $l$ attached to the floor by a frictionless hinge as shown. A horizontal spring with force constant $k$ connects the other end of the rod to a vertical wall. The rod is in a uniform magnetic field B directed in to the plane of the figure. There is a current $i$ in the rod as shown and at equilibrium rod makes $53°$ angle with the floor. The energy stored by the spring in equilibrium is

A simplified diagram of an electric motor is as shown. The loop of wire is horizontal in a horizontal magnetic field. 

In which direction is the force on side $\mathrm{Y}$ of the wire loop?

Lorentz force is given by: (symbols have their usual meanings)

A uniform magnetic field pointing top to bottom in a plane of paper. When an electron is allowed to move perpendicular to it, it gets deflected outwards. The electron must be moving along:

What is the unit of magnetic field intensity?

A long wire carrying a current of $8 \mathrm{A}$ is placed in a uniform magnetic field of $1.2 \mathrm{T}$. The direction of the field makes an angle $\theta$ with the direction of the current. The force experienced by a$50 \mathrm{cm}$ segment of the wire is found to be $2.4 \mathrm{N}$. If the wire is rotated so that the angle between the direction of the field and that of the current becomes $2\theta$, then the force on the segment of the wire would be