A plane electromagnetic wave of frequency \(100\, MHz\) is travelling in vacuum along the \(x -\) direction. At a particular point in space and time, \(\overrightarrow{ B }=2.0 \times 10^{-8} \hat{ k } T\). (where, \(\hat{ k }\) is unit vector along \(z-\)direction) What is \(\overrightarrow{ E }\) at this point ?

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal place: \((i)\) a ring of radius \(R,\,(ii)\) a solid cylinder of radius \(\frac {R}{2}\)  nd \((iii)\) a solid sphere of radius \(\frac {R}{4}.\) If, in each case, the speed of the center of mass at bottom of the incline is same, the ratio of the maximum heights they climb is

A capacitor of reactance \(4 \sqrt{3} \Omega\) and a resistor of resistance \(4 \Omega\) are connected in series with an ac source of peak value \(8 \sqrt{2} \mathrm{~V}\). The power dissipation in the circuit is _______ \(W\).

Mobility of electron in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an \(n-\) type semiconductor, the density of electrons is \(10^{19}\, m^{-3}\) and their mobility is \(1.6\, m^2\,/(V.s)\) then the resistivity of the semiconductor(since it is an \(n-\) type semiconductor contribution of holes is ignored) is close to ................ \(\Omega  m\)

A body of mass \(1\,kg\) collides head on elastically with a stationary body of mass \(3\,kg\). After collision, the smaller body reverses its direction of motion and moves with a speed of \(2\,m / s\). The initial speed of the smaller body before collision is \(..........ms ^{-1}\)

Three rods of Copper, Brass and Steel are welded together to form a \(Y\) shaped structure. Area of cross - section of each rod \(= 4\ cm^2\) . End of copper rod is maintained at \(100^o C \) where as ends ofbrass and steel are kept at \(0^o C\). Lengths of the copper, brass and steel rods are \(46, 13\) and \(12\ cms\) respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are \(0.92, 0.26\) and \(0.12\ CGS\) units respectively. Rate ofheat flow through copper rod is ....... \(cal\, s^{-1}\)

A body of mass \(5 \mathrm{~kg}\) moving with a uniform speed \(3 \sqrt{2} \mathrm{~ms}^{-1}\) in \(\mathrm{X}-\mathrm{Y}\) plane along the line \(\mathrm{y}=\mathrm{x}+4\).The angular momentum of the particle about the origin will be _______ \(\mathrm{kg}\  \mathrm{m} \mathrm{s}^{-1}\).

A parallel plate capacitor with plates of area \(1\,m^2\) each, are at a separation of \(0.1\,m.\) If the electric field between the plates is \(100\,N/C,\) the magnitude of charge on each plate

A plane is inclined at an angle \(\alpha  = 30^o\) with respect to the horizontal. A particle is projected with a speed \(u = 2\,ms^{-1},\) from the base of the plant, making an angle \(\theta = 15^o\) with respect to the plane as shown in the figure. The distance from the base at which the particle hits the plane is close to  ........ \(cm\) (Take \(g = 10\,ms^2\) )

A bob of mass \(m\) attached to an inextensible string of length \(l\) is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed \(\omega\ rad/s\) about the vertical. About the point of suspension:

The half-life of \(Au ^{198}\) is \(2.7\, days.\) The activity of \(1.50\, mg\) of \(Au ^{198}\) if its atomic weight is \(198\, g mol ^{-1}\) is .......\(Ci\) \(\left( N _{ A }=6 \times 10^{23}\, / mol \right)\)

A particle is projected with velocity \(u\) so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as \(\frac{n u^2}{25 g}\), where value of \(n\) is : (Given ' \(g\) ' is the acceleration due to gravity).

The energy associated with electric field is \((U_E)\) and with magnetic field is \((U_B)\) for an electromagnetic wave in free space. Then