A magnetic dipole in a constant magnetic field has 

A slit of width \(a\) is illuminated by light of wavelength \(\lambda\). The linear separation between \(1^{st}\) and \(3^{rd}\) minima in the diffraction pattern produced on a screen placed at a distance \(D\) from the slit system is _____.

A ball of mass \(200\,g\) rests on a vertical post of height \(20\,m\). A bullet of mass \(10\,g\), travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance \(30\,m\) and the bullet at a distance of \(120\,m\) from the foot of the post. The value of initial velocity of the bullet will be \(............m/s\) (if \(\left.g =10 m / s ^2\right)\)

A spherically symmetric charge distribution is considered with charge density varying as \(\rho(r)=\left\{\begin{array}{ll}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text { for } r \leq R \\ \text { Zero } & \text { for } r>R\end{array}\right.\) Where, \(r ( r < R )\) is the distance from the centre \(O\) (as shown in figure). The electric field at point \(P\) will be.

The effective resistance between \(A\) and \(B\), if resistance of each resistor is \(R\) will be _______.

A particle is moving in a straight line. The variation of position ' \(x\) ' as a function of time ' \(t\) ' is given as \(x=\left(t^3-6 t^2+20 t+15\right) m\). The velocity of the body when its acceleration becomes zero is _______.

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, \(\mathrm{y}_1(\mathrm{x}, \mathrm{t})=4 \sin (\mathrm{kx}-\omega \mathrm{t})\) and \(\mathrm{y}_2(\mathrm{x}, \mathrm{t})=2 \sin \left(\mathrm{kx}-\omega \mathrm{t}+\frac{2 \pi}{3}\right)\), are \(:\)
(Take the angular frequency of initial waves same as \(\omega\))

A magnetic field vector in an electromagnetic wave is represented by \(\vec{B}=B_0\sin\left(2\pi vt-\dfrac{2\pi x}{\lambda}\right)\hat{j}\). Its associated electric field vector is ______.

The magnetic field existing in a region is given by \(\overrightarrow{\mathrm{B}}=0.2(1+2 \mathrm{x}) \hat{\mathrm{k} T}\). A square loop of edge \(50 \mathrm{~cm}\) carrying \(0.5 \mathrm{~A}\) current is placed in \(x-y\) plane with its edges parallel to the \(x-y\) axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is___________ \(\mathrm{mN}\).

A body of mass \(0.5\, kg\) travels on straight line path with velocity \(v =\left(3 x ^{2}+4\right) m / s\). The net workdone by the force during its displacement from \(x =0\) to \(x =2\, m\) is\(.......J\)