A solenoid of $1000$ turns per metre has a core with relative permeability $500$. Insulated windings of the solenoid carry an electric current of $5\, A$. The magnetic flux density produced by the solenoid is
(permeability of free space $\left.=4 \pi \times 10^{-7} H / m \right)$
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The current in the windings of a toroid is $2.0\,A$. There are $400\,turns$ and the mean circumferential length is $40\,cm$. If the inside magnetic field is $1.0\,T,$ the relative permeability is near to
A galvanometer with a resistance of $12 \,\Omega$ gives full scale deflection when a current of $3\, mA$ is passed. It is required to convert it into a voltmeter which can read up to $18\, V$. the resistance to be connected is ............... $\Omega $
Wires $1$ and $2$ carrying currents ${i_1}$ and ${i_2}$respectively are inclined at an angle $\theta $ to each other. What is the force on a small element $dl$ of wire $2$ at a distance of $r$ from wire $1$ (as shown in figure) due to the magnetic field of wire $1$
A particle of mass $M$ and charge $Q$ moving with velocity $\mathop v\limits^ \to $ describes a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B$. The work done by the field when the particle completes one full circle is
An $\alpha$-particle (mass $4 amu$ ) and a singly charged sulfur ion (mass $32 amu$ ) are initially at rest. They are accelerated through a potential $V$ and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the $\alpha$-particle and the sulfur ion move in circular orbits of radii $r_\alpha$ and $r_5$, respectively. The ratio $\left(r_s / r_\alpha\right)$ is. . . . .$(4)$
A conducting ring of mass $2\,\, kg$ and radius $0.5\,\ m$ is placed on a smooth horizontal plane. The ring carries a current $i = 4A. A$ horizontal magnetic field $B = 10T$ is switched on at time $t = 0$ as shown in figure. The initial angular acceleration of the ring will be
A metallic block carrying current $I$ is subjected to a uniform magnetic induction $\overrightarrow B $ as shown in the figure. The moving charges experience a force $\overrightarrow F $ given by ........... which results in the lowering of the potential of the face ........ Assume the speed of the carriers to be $v$