A long, straight wire of radius \(a\) carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance \(\frac{a}{3}\) and \(2 a,\) respectively from the axis of the wire is

Consider an electron in a hydrogen atom, revolving in its second excited state (having radius \(4.65\, \mathop A\limits^o \)). The de-Broglie wavelength of this electron is....\(\mathop A\limits^o \)

In a given circuit diagram, a \(5 \,{V}\) zener diode along with a series resistance is connected across a \(50 \,V\) power supply. The minimum value of the resistance required, if the maximum zener current is \(90\, {mA}\) will be \(.....\,\Omega .\)

In an experiment to determine the Young's modulus, steel wires of five different lengths \((1,2,3,4\) and \(5\,m )\) but of same cross section \(\left(2\,mm ^{2}\right)\) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is \(x \times 10^{11}\,Nm ^{-2}\), then the value of \(x\) is

A thermodynamic system is taken from an original state \(A\) to an intermediate state \(B\) by a linear process as shown in the figure. It's volume is then reduced to the original value from \(B\) to \(C\) by an isobaric process. The total work done by the gas from \(A\) to \(B\) and \(B\) to \(C\) would be :

A uniform metallic wire carries a current \(2\,A\). when \(3.4\,V\) battery is connected across it. The mass of uniform metallic wire is \(8.92 \times 10^{-3} \,kg\). density is \(8.92 \times 10^3\,kg / m ^3\) and resistivity is \(1.7 \times 10^{-8} \Omega- m\). The length of wire is \(l=............\,m\)

For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant \(K\) is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is \(\frac{3}{4} d\), where \('d'\) is the separation between the plates of parallel plate capacitor. The new capacitance \((C')\) in terms of original capacitance \(\left( C _{0}\right)\) is given by the following relation

As shown in the figure, a particle is moving with constant speed \(\pi\,m / s\). Considering its motion from \(A\) to \(B\), the magnitude of the average velocity is:

The potential energy function (in J) of a particle in a region of space is given as \(U=\left(2 x^2+3 y^3+2 z\right)\). Here \(\mathrm{x}, \mathrm{y}\) and \(\mathrm{z}\) are in meter. The magnitude of \(\mathrm{x}\) - component of force (in \(\mathrm{N}\) ) acting on the particle at point \(\mathrm{P}(1,2,3)\ \mathrm{m}\) is:

Three parallel plate capacitors each with area A and separation d are filled with two dielectric ( \(k _1\) and \(k _2\) ) in the following fashion. Which of the following is true? \(\left( k _1> k _2\right)\)

In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman series is \(304\,\mathring {A}.\) The corresponding difference for the Paschan series in \(\mathring {A}\) is