An electric dipole of dipole moment is \(6.0 \times 10^{-6}\,Cm\) placed in a uniform electric field of \(1.5 \times 10^3\,NC ^{-1}\) in such a way that dipole moment is along electric field. The work done in rotating dipole by \(180^{\circ}\) in this field will be \(.........\,mJ\)

An electric dipole of moment \(\overrightarrow{\mathrm{p}}=(-\hat{\mathrm{i}}-3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}) \times 10^{-29}\; \mathrm{C} \cdot \mathrm{m}\) is at the origin \((0,0,0) .\) The electric field due to this dipole at \(\overrightarrow{\mathrm{r}}=+\hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}\) (note that \(\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{p}}=0)\) is parallel to

A green light is incident from the water to the air - water interface at the critical angle \((\theta)\). Select the correct statement .

For an ideal heat engine, the temperature of the source is \(127\,^{\circ} C\). In order to have \(60\, \%\) efficiency the temperature of the sink should be \(........\,{ }^{\circ} C\). (Round off to the Nearest Integer)

At time \(t =0\) a particle starts travelling from a height \(7\,\hat{z} cm\) in a plane keeping \(z\) coordinate constant. At any instant of time it's position along the \(x\) and \(y\) directions are defined as \(3\,t\) and \(5\,t^{3}\) respectively. At \(t =1\,s\) acceleration of the particle will be.

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors \(\overrightarrow{ a }, \overrightarrow{ b }\) and \(\overrightarrow{ c }\) respectively. Then choose the correct relation for these vectors.

Electric field in a region is given by \( \vec{E}=Ax\hat{i}+By\hat{j} \), where \( A=10~V/m^{2} \) and \( B=5~V/m^{2} \). If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is __________ V.

A closely wounded circular coil of radius \(5\,cm\) produces a magnetic field of \(37.68 \times 10^{-4}\,T\) at its center. The current through the coil is \(......A\). [Given, number of turns in the coil is \(100\) and \(\pi=3.14]\)

Water droplets are coming from an open tap at particular rate. The spacing between a droplet observed at \(4^{{th}}\;second\) after its fall to the next droplet is \(34.3 \,{m}\). At what rate the droplets are coming from the tap ? (Take \(g=9.8\, {m} / {s}^{2}\))

One of the two identical conducing wires of length \(L\) is bent in the form of a circular loop and the other one into a circular coil of \(N\) identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop \((B_L)\) to that at the centre of the coil \((B_C),\); \(.\,\frac {B_L}{B_C}\) will be

A disc with a flat small bottom beaker placed on it at a distance \(R\) from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity \(\omega\). The coefficient of static friction between the bottom of the beaker and the surface of the disc is \(\mu\). The beaker will revolve with the disc if 

The current in a conductor is expressed as \(I=3 t^2+4 t^3\), where \(I\) is in Ampere and \(t\) is in second. The amount of electric charge that flows through a section of the conductor during \(t=1\) s to \(t=2 \mathrm{~s}\) is _______ \(\mathrm{C}\).

A constant magnetic field of \(1 \,{T}\) is applied in the \({x}\,>\,0\) region. A metallic circular ring of radius \(1 \,{m}\) is moving with a constant velocity of \(1 \,{m} / {s}\) along the \(x\)-axis. At \(t=0\) \(s,\) the centre of \(O\) of the ring is at \({x}=-1 \,{m}\). What will be the value of the induced \(emf\) in the ring at \(t=1\, s\) ? (Assume the velocity of the ring does not change.) (In \({V}\))