Find the magnetic field at point \(P\) due to a straight line segment \(AB\) of length \(6\, cm\) carrying a current of \(5\, A\). (See figure) \((\mu _0 = 4p\times10^{-7}\, N-A^{-2})\)

In a moving coil galvanometer, two moving coils \(M_1\) and \(M_2\) have the following particulars :
\(\begin{aligned}
& \mathrm{R}_1=5 \Omega, \mathrm{~N}_1=15, \mathrm{~A}_1=3.6 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_1=0.25 \mathrm{~T} \\
& \mathrm{R}_2=7 \Omega, \mathrm{~N}_2=21, \mathrm{~A}_2=1.8 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_2=0.50 \mathrm{~T}
\end{aligned}\)
Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of \(M_1\) and \(M_2\) ?

The resistance of the meter bridge \(AB\) in given figure is \(4\,\Omega \). With a cell of emf  \(\varepsilon \, = 0.5\,\,V\) and rheostat resistance \(R_h = 2\,\Omega \) the null point is obtained at some point \(J.\) When the cell is replaced by another one of emf \(\varepsilon \, = {\varepsilon _2}\) the same null point \(J\) is found for \(R_h = 6\,\Omega .\) The \(emf\)  \({\varepsilon _2}\) is ................. \(V\)

A hydrogen atom in is ground state absorbs \(10.2\;eV\) of energy. The angular momentum of electron of the hydrogen atom will increase by the value of ............... \(\times 10^{-34} \; J {s}\) (Given, Plank's constant \(\left.=6.6 \times 10^{-34} Js \right)\)

The top of a water tank is open to air and its water level is maintained. It is giving out \(0.74\,m^3\) water per minute through a circular opening of \(2\,cm\) radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to........ \(m\)

Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have common axis. The current through P and Q are I and 4I respectively in clockwise direction as seen from O . The net magnetic field at O is:

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as \(4.62 \mathrm{~s}, 4.632 \mathrm{~s}, 4.6 \mathrm{~s}\) and \(4.64 \mathrm{~s}\). The arithmetic mean of these reading in correct significant figure is _______.

Two charges of \(5 Q\) and \(-2 Q\) are situated at the points \((3 a, 0)\) and \((-5 a, 0)\) respectively. The electric flux through a sphere of radius \(4a\) having center at origin is

If a copper wire is stretched to increase its length by \(20 \% \). The percentage increase in resistance of the wire is \(..........\%\)

Two wavelengths \(\lambda_1\) and \(\lambda_2\) are used in Young's double slit experiment \(\lambda_1=450 \mathrm{~nm}\) and \(\lambda_2=650 \mathrm{~nm}\). The minimum order of fringe produced by \(\lambda_2\) which overlaps with the fringe produced by \(\lambda_1\) is \(n\). The value of \(n\) is _________.

A smooth wire of length \(2\pi r\) is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed \(\omega\) about the vertical diameter \(AB\), as shown in figure, the bead is at rest with respect to the circular ring at position \(P\) as shown. Then the value of \(\omega^2\) is equal to

A coil of area A and N turns is rotating with angular velocity \(\omega\) in a uniform magnetic field \(\vec{B}\) about an axis perpendicular to \(\vec{B}\). Magnetic flux \(\varphi\) and induced \(\operatorname{emf} \varepsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :

The time dependence of the position of a particle of mass \(m = 2\) is given by \(\vec r\,(t)\, = \,2t\,\hat i\, - 3{t^2}\hat j\) Its angular momentum with respect to the origin at time \(t = 2\) is