A capacitor is connected to a 20 V battery through a resistance of 10$$\Omega$$. It is found that the potential difference across the capacitor rises to 2 V in 1 $$\mu$$s. The capacitance of the capacitor is __________ $$\mu$$F. Given : \ln \left( {{{10} \over 9}} \right) = 0.105

Which of the following equations represents a travelling wave?

A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is :

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

A sound wave of frequency 245 Hz travels with the speed of 300 ms$$-$$1 along the positive x-axis. Each point of the wave moves to and from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?

The motion of a mass on a spring, with spring constant K is as shown in figure. The equation of motion is given by x(t) = A sin$$\omega$$t + B cos$$\omega$$t with $$\omega$$ = \sqrt {{K \over m}} Suppose that at time t = 0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t) = C cos($$\omega$$t $$-$$ $$\varphi$$), where C and $$\varphi$$ are :

A proton, a deuteron and an $$\alpha$$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is _________ and their speed is _______, in the ratio.

Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is ________.

A charge Q is moving $$\overrightarrow{dl}$$ distance in the magnetic field $$\overrightarrow{B}$$. Find the value of work done by $$\overrightarrow{B}$$.

A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5A. The magnetic flux density produced by the solenoid is : (permeability of free space = 4$$\pi$$ $$\times$$ 10$$-$$7 H/m)

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle?

Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the center of A is 3T, the field at the center of C would be : (Assume that the magnetic field is confined with in the volume of respective solenoid).

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

A proton and an $$\alpha$$-particle, having kinetic energies Kp and K$$\alpha$$ respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of $$\alpha$$-particle is 2 : 1. The ratio of Kp : K$$\alpha$$ is :

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let rd and r$$\alpha$$ be their respective radii of circular path. The value of {{{r_d}} \over {{r_\alpha }}} is equal to :

Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :

Figure A and B shown to long straight wires of circular cross-section (a and b with a < b), carrying current I which is uniformly distributed across the cross-section. The magnitude of magnetic field B varies with radius r and can be represented as :

The fractional change in the magnetic field intensity at a distance 'r' from centre on the axis of current carrying coil of radius 'a' to the magnetic field intensity at the centre of the same coil is : (Take r < a)

Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :

A coaxial cable consists of an inner wire of radius 'a' surrounded by an outer shell of inner and outer radii 'b' and 'c' respectively. The inner wire carries an electric current i0, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance x from the axis when (i) x < a and (ii) a < x < b ?