Magnetics

A particle of mass $M$ and charge $Q$ moving with velocity $\overrightarrow v$ describe a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B.$ The network done by the field when the particle completes one full circle is

A charged particle of mass $m$ and charge $q$ travels on a circular path of radius $r$ that is perpendicular to a magnetic field $B.$ The time taken by the particle to complete one revolution is

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a

A current $i$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

A current $I$ flows along the length of an infinitely long, straight, thin walled pipe. Then

A long straight wire of radius $a$ carries a steady current $i.$ The current is uniformly distributed across its cross section. The ratio of the magnetic field at $a/2$ and $2a$ is

A long solenoid has $200$ turns per $cm$ and carries a current $i.$ The magnetic field at its center is $6.28 \times {10^{ - 2}}\,\,\,Weber/{m^2}.$ Another long solenoid has $100$ turns per $cm$ and it carries a current ${i \over 3}$. The value of the magnetic field at its center is

A long, straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance ${a \over 3}$ and 2$a$, respectively from the axis of the wire is :

A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its centre will be :

Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below :

A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2 a$ from axis of the wire is :

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :

If in a circular coil $A$ of radius $R,$ current $I$ is flowing and in another coil $B$ of radius $2R$ a current $2I$ is flowing, then the ratio of the magnetic fields ${B_A}$ and ${B_B}$, produced by them will be

If a current is passed through a spring then the spring will

The magnetic field due to a current carrying circular loop of radius $3$ $cm$ at a point on the axis at a distance of $4$ $cm$ from the centre is $54\,\mu T.$ What will be its value at the center of loop?

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $B.$ It is then bent into a circular loop of $n$ turns. The magnetic field at the center of the coil will be

Two concentric coils each of radius equal to $2$ $\pi$ $cm$ are placed at right angles to each other. $3$ ampere and $4$ ampere are the currents flowing in each coil respectively . The magnetic induction in Weber / ${m^2}$ at the center of the coils will be $\left( {\mu = 4\pi \times {{10}^{ - 7}}Wb/A.m} \right)$

Two identical conducting wires $AOB$ and $COD$ are placed at right angles to each other. The wire $AOB$ carries an electric current ${I_1}$ and $COD$ carries a current ${I_2}$. The magnetic field on a point lying at a distance $d$ from $O$, in a direction perpendicular to the plane of the wires $AOB$ and $COD$ , will be given by