A conducting wire bent in the form of a parabola $y^2 = 2x$ carries a current $i = 2 A$ as shown in figure. This wire is placed in a uniform magnetic field $\vec B = - 4\,\hat k$ $Tesla$. The magnetic force on the wire is (in newton)
$ - 16\,\hat i$
$ 32\,\hat i$
$ - 32\,\hat i$
$ 16\,\hat i$
Currents of a $10\, ampere$ and $2\, ampere$ are passed through two parallel thin wires $A$ and $B$ respectively in opposite directions. Wire $A$ is infinitely long and the length of the wire $B$ is $2\, m$. The force acting on the conductor $B$, which is situated at $10\, cm$ distance from $A$ will be
A solenoid $60 \;cm$ long and of radius $4.0\; cm$ has $3$ layers of windings of $300$ turns each. A $2.0 \;cm$ long wire of mass $2.5\; g$ lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of $6.0\; A$ in the wire. What value of current (with appropriate sense of circulation in $A$) in the windings of the solenoid can support the weight of the wire? $g=9.8\; m \,s ^{-2}$
A $2 \mathrm{~A}$ current carrying straight metal wire of resistance $1 \Omega$, resistivity $2 \times 10^{-6} \Omega \mathrm{m}$, area of cross-section $10 \mathrm{~mm}^2$ and mass $500 \mathrm{~g}$ is suspended horizontally in mid air by applying a uniform magnetic field $\vec{B}$. The magnitude of $B$ is__________.$\times 10^{-1} \mathrm{~T}\left(\right.$ given, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
A large current carrying plate is kept along $y-z$ plane with $k$ $amp$ current per unit length in the $+ve$ $y$ direction. Find the net force on the semi cricular current carrying looplying in the $x-y$ plane. Radius of loop is $R$, current is $i$ and centre is at $(d,0, 0)$ where $(d > R)$
A charge of $2.0\,\mu C$ moves with a speed of $3.0 \times {10^6}\,m{s^{ - 1}}$ along $+ ve$ $X$ - axis $A$ magnetic field of strength $\vec B = - 0.2\,\,\hat k$ $Tesla$ exists in space. What is the magnetic force $({\overrightarrow F _m})$ on the charge