Advertisements
Advertisements
प्रश्न
A block of mass containing a net positive charge q is placed on a smooth horizontal table which terminates in a vertical wall as shown in the figure. The distance of the block from the wall is d. A horizontal electric field E towards the right is switched on. Assuming elastic collisions (if any), find the time period of the resulting oscillatory motion. Is it a simple harmonic motion?
उत्तर
For motion to be simple harmonic,acceleration should be proportional to the displacement and should be directed in a direction opposite to the displacement.
When the block is moving towards the wall, the acceleration is along displacement.
So, the block does not undergo SHM.
Time taken to reach the wall is given by
\[d = ut + \frac{1}{2}a t^2 \]
\[ \Rightarrow t = \sqrt{\frac{2\text{md}}{qE}} (\text{ Using u = 0, and } a = \frac{qE}{m})\]
Since it is an elastic collision, the time taken by the block to move towards the wall is the time taken to move away from it till the velocity is zero.
Total time, T = 2t
\[\Rightarrow T = 2\sqrt{\frac{2dm}{qE}} = \sqrt{\frac{8dm}{qE}}\]
APPEARS IN
संबंधित प्रश्न
plot a graph showing the variation of current density (j) versus the electric field (E) for two conductors of different materials. What information from this plot regarding the properties of the conducting material, can be obtained which can be used to select suitable materials for use in making (i) standard resistance and (ii) connecting wires in electric circuits?
Plot a graph showing the variation of resistivity of a conductor with temperature.
A metallic particle with no net charge is placed near a finite metal plate carrying a positive charge. The electric force on the particle will be
A charge Q is uniformly distributed over a rod of length l. Consider a hypothetical cube of edge l with the centre of the cube at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube.
The electric field in a region is given by
`vec"E"= 3/5"E"_0 vec"i" + 4/5 "E"_0 vec "i" "with" " E"_0 = 2.0 xx 10^3 "N""C"^-1.`
Find the flux of this field through a rectangular surface of area 0⋅2 m2 parallel to the y-z plane.
The radius of a gold nucleus (Z = 79) is about 7.0 × 10-10 m. Assume that the positive charge is distributed uniformly throughout the nuclear volume. Find the strength of the electric field at (a) the surface of the nucleus and (b) at the middle point of a radius. Remembering that gold is a conductor, is it justified to assume that the positive charge is uniformly distributed over the entire volume of the nucleus and does not come to the outer surface?
A charged particle with a charge of −2⋅0 × 10−6 C is placed close to a non-conducting plate with a surface charge density of 4.0 × 10-6Cm0-2. Find the force of attraction between the particle and the plate.
Two conducting plates X and Y, each with a large surface area A (on one side), are placed parallel to each other, as shown in the following figure . Plate X is given a charge Q,whereas the other is kept neutral. Find (a) the surface charge density at the inner surface of plate X (b) the electric field at a point to the left of the plates (c) the electric field at a point in between the plates and (d) the electric field at a point to the right of the plates.
Three identical metal plates with large surface areas are kept parallel to each other as shown in the following figure. The leftmost plate is given a charge Q, the rightmost a charge −2Q and the middle one is kept neutral. Find the charge appearing on the outer surface of the rightmost plate.
A uniform electric field of 10 N C−1 exists in the vertically downward direction. Find the increase in the electric potential as one goes up through a height of 50 cm.
Consider a circular ring of radius r, uniformly charged with linear charge density λ. Find the electric potential at a point on the axis at a distance x from the centre of the ring. Using this expression for the potential, find the electric field at this point.
A uniform field of 2.0 NC−1 exists in space in the x-direction. (a) Taking the potential at the origin to be zero, write an expression for the potential at a general point (x, y, z). (b) At which point, the potential is 25 V? (c) If the potential at the origin is taken to be 100 V, what will be the expression for the potential at a general point? (d) What will be the potential at the origin if the potential at infinity is taken to be zero? Is it practical to choose the potential at infinity to be zero?
Answer the following question.
Prove that the average energy density of the oscillating electric field is equal to that of the oscillating magnetic field.
A simple pendulum consists of a small sphere of mass m suspended by a thread of length l. The sphere carries a positive charge q. The pendulum is placed in a uniform electric field of strength E directed vertically downwards. Find the period of oscillation of the pendulum due to the electrostatic force acting on the sphere, neglecting the effect of the gravitational force.
A charge Q is applied to a conducting sphere of radius R. At the sphere's centre, the electric potential and electric field are respectively
Pick out the statement which is incorrect
