Advertisements
Advertisements
Question
A block of mass m with a charge q is placed on a smooth horizontal table and is connected to a wall through an unstressed spring of spring constant k, as shown in the figure. A horizontal electric field E, parallel to the spring, is switched on. Find the amplitude of the resulting SHM of the block. 
Advertisements
Solution
Given:
Charge of the block = q
Electrical field intensity = E
Mass of the block = m
Spring constant = k
Electric force, F = qE
Spring force, F = − kx (where x is the amplitude)
Therefore, qE = − kx
\[\Rightarrow x = \left| - \frac{qE}{k} \right| = \frac{qE}{k}\]
APPEARS IN
RELATED QUESTIONS
The figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

A hollow cylindrical box of length 1 m and area of cross-section 25 cm2 is placed in a three dimensional coordinate system as shown in the figure. The electric field in the region is given by `vecE = 50xhati` where E is NC−1 and x is in metres. Find
(i) Net flux through the cylinder.
(ii) Charge enclosed by the cylinder.

The electric field at the origin is along the positive x-axis. A small circle is drawn with the centre at the origin, cutting the axes at points A, B, C and D with coordinates (a, 0), (0, a), (−a, 0), (0, −a), respectively. Out of the points on the periphery of the circle, the potential is minimum at
The electric field in a region is directed outward and is proportional to the distance rfrom the origin. Taking the electric potential at the origin to be zero,
A particle of mass 1 g and charge 2.5 × 10−4 C is released from rest in an electric field of 1.2 × 10 4 N C−1. What will be the speed of the particle after travelling this distance?
A ball of mass 100 g and with a charge of 4.9 × 10−5 C is released from rest in a region where a horizontal electric field of 2.0 × 104 N C−1 exists. (a) Find the resultant force acting on the ball. (b) What will be the path of the ball? (c) Where will the ball be at the end of 2 s?
An electric field of 20 NC−1 exists along the x-axis in space. Calculate the potential difference VB − VA where the points A and B are
(a) A = (0, 0); B = (4 m, 2m)
(b) A = (4 m, 2 m); B = (6 m, 5 m)
(c) A = (0, 0); B = (6 m, 5 m)
Do you find any relation between the answers of parts (a), (b) and (c)?
An electric field \[\vec{E} = \vec{i}\] Ax exists in space, where A = 10 V m−2. Take the potential at (10 m, 20 m) to be zero. Find the potential at the origin.
Find the magnitude of the electric field at the point P in the configuration shown in the figure for d >> a.
Which of the following methods can be used to charge a metal sphere positively without touching it? Select the most appropriate.
The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the center of the disc is `sigma/(2∈_0)`. With respect to the field at the center, the electric field along the axis at a distance R from the center of the disc ______.
Two identical blocks are kept on a frictionless horizontal table connected by a spring of stiffness k and of original length l0. A total charge Q is distributed on the block such that maximum elongation of spring at equilibrium is equal to x. Value of Q is ______.
Two similar spheres having +Q and -Q charges are kept at a certain distance. F force acts between the two. If at the middle of two spheres, another similar sphere having +Q charge is kept, then it experiences a force in magnitude and direction as ______.
The Electric field at a point is ______.
- always continuous.
- continuous if there is no charge at that point.
- discontinuous only if there is a negative charge at that point.
- discontinuous if there is a charge at that point.
For a system of n point charges, what is the mathematical expression for the total electric field at point P?
What does the symbol ε₀ represent in the electric field formula?
In the electric field formula, what does the symbol \[\hat r_i\]P represent?
