A long solenoid has $200$ $turns$ per $cm$ and carries a current $i$. The magnetic field at its centre is $6.28 \times 10^{-2} $ $\frac{{Wb}}{{{m^2}}}$ Another long solenoid has $100$ $turns$ per $cm$ and it carries a current $\frac{I}{3}\;$ . The value of the magnetic field at its centre is
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A semi circular current carrying wire having radius $R$ is placed in $x-y$ plane with its centre at origin $‘O’$. There is non-uniform magnetic $\vec B = \frac{{{B_o}x}}{{2R}}\hat k$ (here $B_o$ is + $ve$ constant) is existing in the region. The magnetic force acting on semi circular wire will be along
The radius of a circular ring of wire is $R$ and it carries a current of $I\,ampere$. At its centre a smaller ring of radius $r$ with current $i$ and $N\, turns$ is placed. Assuming that the planes of two rings are perpendicular to each other and the magnetic induction produced at the centre of bigger ring is constant, then the torque acting on smaller ring will be
A long straight metal rod has a very long hole of radius $‘a’$ drilled parallel to the rod axis as shown in the figure. If the rod carries a current $‘i’$ find the value of magnetic induction on the axis of the hole, where $OC = c$
A conducting ring of radius $'r$' is placed in a varying magnetic field perpendicular to the plane of the ring, the rate at which magnetic field varies is $x$ the electric field intensity at any point of the ring is
A galvanometer having a resistance of $20\,\Omega $ and $30\, divisions$ on both sides has figure of merit $0.005\, ampere /division$. The resistance that should be connected in series such that it can be used as a voltmeter upto $15\, volt$ is ........... $\Omega$
A straight wire of length $0.5\, metre$ and carrying a current of $1.2\, ampere$ placed in a uniform magnetic field of induction $2\, Tesla$. The magnetic field is perpendicular to the length of the wire. The force on the wire is.......$N$