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 $OC = c$
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Two circular coils $X$ and $Y$, having equal number of turns, carry equal currents in the same sence and subtend same solid angle at point $O$. If the smaller coil $X$ is midway between $O$ and $Y$, and If we represent the magnetic induction due to bigger coil $Y$ at $O$ as $B_Y$ and that due to smaller coil $X$ at $O$ as $B_X$, then $\frac{{{B_Y}}}{{{B_X}}}$ is
The circuit in figure consists of wires at the top and bottom and identical springs as the left and right sides. The wire at the bottom has a mass of $10\, g$ and is $5\, cm$ long. The wire is hanging as shown in the figure. The springs stretch $0.5\, cm$ under the weight of the wire and the circuit has a total resistance of $12\, \Omega $. When the lower wire is subjected to a static magnetic field, the springs, stretch an additional $0.3\, cm$. The magnetic field is
A current of $3$ $amp$ is flowing in a plane circular coil of radius $4\, cm$ and number of turns $20$. The coil is placed in a uniform magnetic field of magnetic induction $0.5\, tesla$. Then, the dipole moment of the coil is.....$A-m^2$
A solenoid of length $0.5 \mathrm{~m}$ has a radius of $1 \mathrm{~cm}$ and is made up of ' $m$ ' number of turns. It carries a current of $5 \mathrm{~A}$. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3} \mathrm{~T}$, then the value of $m$ is :
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
A magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{j}}$ exists in the region $\mathrm{a} < \mathrm{x} < 2 \mathrm{a}$ and $\vec{B}=-B_0 \hat{j}$, in the region $2 \mathrm{a} < \mathrm{x} < 3 \mathrm{a}$, where $\mathrm{B}_0$ is a positive constant. $\mathrm{A}$ positive point charge moving with a velocity $\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\dot{i}}$, where $v_0$ is a positive constant, enters the magnetic field at $x=a$. The trajectory of the charge in this region can be like,
A battery is connected between two points $A$ and $B$ on the circumference of a uniform conducting ring of radius $r$ and resistance $R$. One of the arcs $AB$ of the ring subtends an angle $\theta $ at the centre. The value of the magnetic induction at the centre due to the current in the ring is
The magnetic field at the centre of a circular coil of radius $r$ carrying current $I$ is ${B_1}$. The field at the centre of another coil of radius $2 r$ carrying same current $I$ is ${B_2}$. The ratio $\frac{{{B_1}}}{{{B_2}}}$ is
A singly ionized magnesium atom $(A=24)$ ion is accelerated to kinetic energy $5\,keV$ and is projected perpendicularly into a magnetic field $B$ of the magnitude $0.5\,T$. The radius of path formed will be___________ $cm$