An electron revolves around an infinite cylindrical wire having uniform linear change density \(2 \times 10^{-8}\,Cm ^{-1}\) in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is \(.........\times 10^6\,ms ^{-1}\). Given mass of electron \(=9 \times 10^{-31}\,kg\)

An electron is moving along \(+x\) direction with a velocity of \(6 \times 10^{6}\, ms ^{-1}\). It enters a region of uniform electric field of \(300 \,V / cm\) pointing along \(+ y\) direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the \(x\) direction will be

Two satellite \(A\) and \(B\) go round a planet in circular orbits having radii \(4 R\) and \(R\) respectively. If the speed of \(\mathrm{A}\) is \(3 v\), the speed of \(\mathrm{B}\) will be _______.

A body of mass \(10 kg\) is projected at an angle of \(45^{\circ}\) with the horizontal. The trajectory of the body is observed to pass through a point \((20,10)\). If \(T\) is the time of flight, then its momentum vector, at time \(t =\frac{ T }{\sqrt{2}}\), is. \(\left[\right.\) Take \(\left.g=10 m / s ^{2}\right]\)

The gap between the plates of a parallel plate capacitor of area \(A\) and distance between plates \(d\), is filled with a dielectric whose permittivity varies linearly from \({ \varepsilon _1}\) at one plate to \({ \varepsilon _2}\) at the other. The capacitance of capacitor is

A point charge of \(+\,12 \,\mu C\) is at a distance \(6 \,cm\) vertically above the centre of a square of side \(12\, cm\) as shown in figure. The magnitude of the electric flux through the square will be ....... \(\times 10^{3} \,Nm ^{2} / C\)

A car of \(800 \mathrm{~kg}\) is taking turn on a banked road of radius \(300 \mathrm{~m}\) and angle of banking \(30^{\circ}\). If coefficient of static friction is \(0.2\) then the maximum speed with which car can negotiate the turn safely which? \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\right)\)

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are \(B_1\) and \(B_2\) respectively, then the ratio \(\dfrac{B_1}{B_2}\) is _______.

The induced \(emf\) can be produced in a coil by \(A.\) moving the coil with uniform speed inside magnetic field \(B.\) moving the coil with non-uniform speed inside uniform magnetic field \(C.\) rotating the coil inside the uniform magnetic field \(D.\) changing the area of the coil inside the uniform magnetic field Choose the correct answer from the options given below:

An inclined plane making an angle of \(30^{\circ}\) with the horizontal is placed in a uniform horizontal electric field \(200 \, \frac{ N }{ C }\) as shown in the figure. A body of mass \(1\, kg\) and charge \(5\, mC\) is allowed to slide down from rest at a height of \(1\, m\). If the coefficient of friction is \(0.2,\) find the time (in \(s\) )taken by the body to reach the bottom. \(\left[ g =9.8 \,m / s ^{2}, \sin 30^{\circ}=\frac{1}{2}\right.\); \(\left.\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right]\)

A body of mass \(5\,kg\) is moving with a momentum of \(10\,kg\,ms ^{-1}\). Now a force of \(2\,N\) acts on the body in the direction of its motion for \(5\,s\). The increase in the Kinetic energy of the body is \(...........J\).