Find the magnetic field at the point $$\mathrm{P}$$ in figure. The curved portion is a semicircle connected to two long straight wires.

A rod with circular cross-section area $$2{\mathrm{cm}}^2$$ and length $$40\mathrm{cm}$$ is wound uniformly with 400 turns of an insulated wire. If a current of $$0.4\mathrm{A}$$ flows in the wire windings, the total magnetic flux produced inside windings is $$4\pi \times 10^{-6}\mathrm{Wb}$$. The relative permeability of the rod is (Given : Permeability of vacuum $${\mu }_0=4\pi \times 10^{-7}{\mathrm{NA}}^{-2}$$)

As shown in the figure, a current of $2\mathrm{A}$ flowing in an equilateral triangle of side $4\sqrt{3}\mathrm{cm}$. The magnetic field at the centroid $\mathrm{O}$ of the triangle is (Neglect the effect of earth's magnetic field)

A current carrying rectangular loop PQRS is made of uniform wire. The length $PR=QS=5\mathrm{cm}$ and $PQ=RS=100\mathrm{cm}$. If ammeter current reading changes from I to $2 I$, the ratio of magnetic forces per unit length on the wire $P Q$ due to wire $R S$ in the two cases respectively $\left(f_{PQ}^I:f_{PQ}^{2t}\right)$ is:

A massless square loop, of wire of resistance $$10\Omega$$, supporting a mass of $$1\mathrm{g}$$, hangs vertically with one of its sides in a uniform magnetic field of $$10^3\mathrm{G}$$, directed outwards in the shaded region. A dc voltage $$\mathrm{V}$$ is applied to the loop. For what value of $$\mathrm{V}$$, the magnetic force will exactly balance the weight of the supporting mass of $$1\mathrm{g}$$ ? (If sides of the loop $$=10\mathrm{cm},\mathrm{g}=10{\mathrm{ms}}^{-2}$$)

The magnetic moments associated with two closely wound circular coils $$\mathrm{A}$$ and $$\mathrm{B}$$ of radius $${\mathrm{r}}_{\mathrm{A}}=10$$ $$\mathrm{cm}$$ and $${\mathrm{r}}_{\mathrm{B}}=20\mathrm{cm}$$ respectively are equal if : (Where $${\mathrm{N}}_{\mathrm{A}},{\mathrm{I}}_{\mathrm{A}}$$ and $${\mathrm{N}}_{\mathrm{B}},{\mathrm{I}}_{\mathrm{B}}$$ are number of turn and current of $$\mathrm{A}$$ and $$\mathrm{B}$$ respectively)

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

The magnitude of magnetic induction at mid point $$\mathrm{O}$$ due to current arrangement as shown in Fig will be

A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve $$\mathrm{z}$$ direction and lying in $$xy$$ plane is shown in figure. The plot of $$\hat{j}$$ component of magnetic field (By) at a distance '$$a$$' (less than radius of the coil) and on $$yz$$ plane vs $$z$$ coordinate looks like

For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passes through it. If the torsional constant of suspension wire is $$4.0\times 10^{-5}\mathrm{N}\mathrm{m}\mathrm{ra}{\mathrm{d}}^{-1}$$, the magnetic field is 0.01T and the number of turns in the coil is 200, the area of each turn (in cm$${}^2$$) is :

Match List I with List II .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} List I (Current configuration) List II (Magnitude of Magnetic Field at point O) A. I. {B_0} = {{{\mu _0}I} \over {4\pi r}}[\pi + 2] B. II. {B_0} = {{{\mu _0}} \over {4 }}{I \over r} C. III. {B_0} = {{{\mu _0}I} \over {2\pi r}}[\pi - 1] D. IV. {B_0} = {{{\mu _0}I} \over {4\pi r}}[\pi + 1] Choose the correct answer from the options given below :

A long solenoid is formed by winding 70 turns cm$${}^{-1}$$. If 2.0 A current flows, then the magnetic field produced inside the solenoid is ____________ ($${\mu }_0=4\pi \times 10^{-7}$$ TmA$${}^{-1}$$)

Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F$${}_1$$. If distance between wires is halved and currents on them are doubled, force F$${}_2$$ on 10 cm length of wire P will be:

A circular loop of radius $$r$$ is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance r from the center of the loop on its axis is :

An electron is moving along the positive $$\mathrm{x}$$-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then A. The electron will experience magnetic force along positive y-axis B. The electron will experience magnetic force along negative y-axis C. The electron will not experience any force in magnetic field D. The electron will continue to move along the positive $$\mathrm{x}$$-axis E. The electron will move along circular path in magnetic field Choose the correct answer from the options given below:

The source of time varying magnetic field may be (A) a permanent magnet (B) an electric field changing linearly with time (C) direct current (D) a decelerating charge particle (E) an antenna fed with a digital signal Choose the correct answer from the options given below:

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid. A. The electron will experience magnetic force along the axis of the solenoid. B. The electron will not experience magnetic force. C. The electron will continue to move along the axis of the solenoid. D. The electron will be accelerated along the axis of the solenoid. E. The electron will follow parabolic path-inside the solenoid. Choose the correct answer from the options given below:

A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle $$30^{\circ }$$, with horizontal. For $${\mu }_s=0.25$$, the block will just start to move for the value of F : [Given $$g=10{\mathrm{ms}}^{-2}$$]