The electric field of an electromagnetic wave in free space is represented as \(\vec{E}=E_0 \cos (\omega t-k z) \hat{i}\). The corresponding magnetic induction vector will be _______.

An observer looks at a distant tree of height \(10\ m\) with a telescope of magnifying power of \(20\). To the observer the tree appears :

A uniform wire (Young's modulus \(2 \times 10^{11}\, Nm^{-2}\) ) is subjected to longitudinal tensile stress of \(5 \times 10^7\,Nm^{-2}\) . If the over all volume change in the wire is \(0.02\%,\) the fractional decrease in the radius of the wire is close to

A lift of mass \(1600\) kg is supported by thick iron wire. If the maximum stress which the wire can withstand is \(4 \times 10^8\) N/m\(^2\) and its radius is \(4\) mm, then maximum acceleration the lift can take is _______ m/s\(^2\). (take \(g = 10\) m/s\(^2\) and \(\pi = 3.14\))

A small square loop of side \('a'\) and one turn is placed inside a larger square loop of side \({b}\) and one turn \((b \gg a)\). The two loops are coplanar with thei centres coinciding. If a current \(I\) is passed in the square loop of side \('b',\) then the coefficient of mutual inductance between the two loops is

As shown in the figure, the voltmeter reads \(2\,V\) across \(5\,\Omega\) resistor. The resistance of the voltmeter is \(.......\,\Omega\).

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is \(1727^{\circ} \mathrm{C}\) and power radiated by the wire is 94.2 W. Its emissivity is \(\frac{x}{8}\) where \(x=\)_______
(Given \(\sigma=6.0 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}, \pi=3.14\) and assume that the emissivity of wire material is same at all wavelength.)

In an electric circuit, a cell of certain emf provides a potential difference of \(1.25\, {V}\) across a load resistance of \(5\, \Omega .\) However, it provides a potential difference of \(1\, {V}\) across a load resistance of \(2\, \Omega\). The \(emf\) of the cell is given by \(\frac{x}{10} v\). Then the value of \(x\) is ..... .

The electric current in a circular coil of \(2\) turns produces a magnetic induction \(B _{1}\) at its centre. The coil is unwound and is rewound into a circular coil of \(5\) turns and the same current produces a magnetic induction \(B _{2}\) at its centre.The ratio of \(\frac{ B _{2}}{ B _{1}}\) is.

The Young's modulus of steel wire of radius \(r\) and length \(L\) is \(Y\). If the radius \(r\) and length \(L\) of the wire are doubled then the value of \(Y\)

A string of area of cross-section \(4\,mm ^{2}\) and length \(0.5\) is connected with a rigid body of mass \(2\,kg\). The body is rotated in a vertical circular path of radius \(0.5\,m\). The body acquires a speed of \(5\,m / s\) at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is \(\ldots . . \times 10^{-5}\). (Use Young's modulus \(10^{11}\,N / m ^{2}\) and \(g =10\,m / s ^{2}\) )