A slab of dielectric constant $$\mathrm{K}$$ has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $$\frac{3}{4}\mathrm{d}$$, where $$\mathrm{d}$$ is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be : (Given $${\mathrm{C}}_0$$ = capacitance of capacitor with air as medium between plates.)

Two identical thin metal plates has charge $$q_1$$ and $$q_2$$ respectively such that $$q_1>q_2$$. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :

A longitudinal wave is represented by x = 10\sin 2\pi \left( {nt - {x \over \lambda }} \right) cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to :

The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be :

If a wave gets refracted into a denser medium, then which of the following is true?

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :

The equations of two waves are given by : y1 = 5 sin 2$$\pi$$(x - vt) cm y2 = 3 sin 2$$\pi$$(x $$-$$ vt + 1.5) cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

Which of the following equations correctly represents a travelling wave having wavelength $$\lambda$$ = 4.0 cm, frequency v = 100 Hz and travelling in positive x-axis direction?

A transverse wave is represented by $$y=2\sin (\omega t-kx)\mathrm{cm}$$. The value of wavelength (in $$\mathrm{cm}$$) for which the wave velocity becomes equal to the maximum particle velocity, will be :

In the wave equation $$y=0.5\sin \frac{2\pi }{\lambda }(400\mathrm{t}-x)\mathrm{m}$$ the velocity of the wave will be:

A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle :

Two long current carrying conductors are placed to each other at a distance of 8 cm between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is 300 $$\mu$$T. The equal current flowing in the two conductors is :

Given below are two statements : Statement I : The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle. Statement II : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below :

Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 $$\times$$ 10$$-$$6 N, then the value of x is approximately :

An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface. Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

Two long parallel conductors S1 and S2 are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure). A charge particle of 3$$\pi$$ coulomb is passing through the point P with velocity $$\overrightarrow{v}=(2\hat{i}+3\hat{j})$$ m/s; where $$\hat{i}$$ and $$\hat{j}$$ represents unit vector along x & y axis respectively. The force acting on the charge particle is $$4\pi \times 10^{-5}(-x\hat{i}+2\hat{j})$$ N. The value of x is :

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is :

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to

A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r

A proton, a deutron and an $$\alpha$$-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :