Question:
Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non-conducting sphere of radius $R$ ?
Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non-conducting sphere of radius $R$ ?
Updated On: Jun 23, 2023
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The electric field intensity at a point lying outside the sphere (non-conducting) is
E = $ \frac{ 1}{ 4 \pi \varepsilon_0} \frac{ q}{ r^2 } $
where r is the distance of that point from centre of sphere.
$ \therefore E \propto \frac{ 1}{r^2} $ $ \hspace20mm$ ..( i)
The electric fieid intensity at surface of sphere
E = $ \frac{ q}{ 4 \pi \varepsilon_0 R^2}$
or $ E \propto \frac{ 1}{R^2} $ $ \hspace20mm$ ..( ii)
R, being the radius of sphere.
The eiectric field intensity at a point Iying inside the sphere is
E = $ \frac{ qr}{ 4 \pi \varepsilon_0 R^3}$
or $ E \propto r $ $ \hspace20mm$ ..( iii)
Also at the centre of sphere r = 0.
Hence, E = 0. The graphical distribution is shown below
Was this answer helpful?
0
0
Top Questions on Electric Charge
- Two point charges of charge \( +q \) each are placed a distance \( 2d \) apart. A grounded solid conducting sphere of radius \( a \) is placed midway between them. Assume \( a^2 \ll d^2 \). Which of the following statements is/are true?
- GATE PH - 2024
- Physics
- Electric Charge
- An electron in the Coulomb field of a proton is in the following state of coherent superposition of orthonormal states \( \psi_{n i m} \):\[ \psi = \frac{1}{3} \psi_{100} + \frac{1}{\sqrt{3}} \psi_{210} + \frac{\sqrt{5}}{3} \psi_{320} \]Let \( E_1, E_2, \) and \( E_3 \) represent the first three energy levels of the system. A sequence of measurements is done on the same system at different times. Energy is measured first at time \( t_1 \) and the outcome is \( E_2 \). Then total angular momentum is measured at time \( t_2 > t_1 \), and finally, energy is measured again at \( t_3 > t_2 \). The probability of finding the system in a state with energy \( E_2 \) after the final measurement is \( \frac{P}{9} \). The value of \( P \) is ______ (in integer).
- GATE PH - 2024
- Physics
- Electric Charge
- A particle of mass \( m \) in an infinite potential well of width \( a \) is subjected to a perturbation \( V' = \frac{h^2}{40ma^2} \) as shown in the figure, where \( h \) is Planck's constant.
The first-order energy shift of the fourth energy eigenstate due to this perturbation is \( \frac{h^2}{Nma^2} \). The value of \( N \) is ____ (in integer).- GATE PH - 2024
- Physics
- Electric Charge
- The curves \( P \) and \( Q \) schematically show the variation of X-ray intensity with wavelength at two different accelerating voltages for a given target material. In the figure, \( \lambda_1 = 0.25 \) Å, \( \lambda_2 = 0.5 \) Å, \( \lambda_3 = 1.0 \) Å, and \( \lambda_4 = 2.25 \) Å. Take Planck's constant as \( 6.6 \times 10^{-34} \) Js, the speed of light as \( 3 \times 10^8 \) m/s, and the elementary charge as \( 1.6 \times 10^{-19} \) C.
Which of the following statement is/are true?- GATE PH - 2024
- Physics
- Electric Charge
- An electron is moving with the speed of \(1\) \(m/s\) at a distance of \(1\) \(m\), from a large sheet of charge with density \(σ\) \(C/m^2\). Find the maximum value of \(σ\) such that electron hits the sheet after \(1\) \(sec\). (mass of electron = \(9 × 10^{-31}\) kg, Permittivity of free space = \(9\times10^{12}\;C^2/Nm^2\)
- JEE Main - 2024
- Physics
- Electric Charge
View More Questions
Questions Asked in Rajasthan PMT exam
- 300 cal of heat is supplied to raise the temperature of 50 g of air from $ 20{}^\circ C $ to $ 30{}^\circ C $ without any change in its volume. Change in internal energy per gram of air is
- Rajasthan PMT - 2011
- internal energy
- The velocity of water flowing in a non-uniform tube is 20 cm/s at a point where the tube radius is 0.2 cm. The velocity at another point, where the radius is 0.1 cm, is
- Rajasthan PMT - 2011
- mechanical properties of fluid
- Block A of mass 4 kg and block B of mass 6 kg are resting on a horizontal surface as shown in the figure. There is no friction between the block B and the horizontal surface. The coefficient of friction between the blocks is 0.2. If the value of $ g=10\,m/{{s}^{2}}, $ the maximum horizontal force F that can be applied on block B without any relative motion between A and B is
- The excess pressure inside a soap bubble A is twice that in another soap bubble B. The ratio of volumes of A and B is
- Rajasthan PMT - 2011
- Surface tension
- The unit of surface tension is
- Rajasthan PMT - 2011
- Surface tension
View More Questions
Concepts Used:
Electric charges and field
What is Electric Charge
It is the property of subatomic particles that experiences a force when put in an electric and magnetic field.
What is Electric Field
It is a property associated with each point in space when charge is present in any form. The magnitude and direction of the electric field are expressed by E, called electric field strength or electric field intensity.
Electric charges are of two types: Positive and Negative. It is commonly carried by charge carriers protons and electrons.
Properties of Electric Charge
Various properties of charge include the following :-
- Additivity of Electric Charge
- Conservation of Electric Charge
- Quantization of Electric Charge
Types of electric charge
Two kinds of electric charges are there :-
Negative Charge - When an object has a negative charge it means that it has more electrons than protons.
Positive Charge - When an object has a positive charge it means that it has more protons than electrons.
When there is an identical number of positive and negative charges, the negative and positive charges would cancel out each other and the object would become neutral.