Assertion : A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal.
Reason : Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field $\overrightarrow B $ in a direction perpendicular to $\overrightarrow B $, will describe circular trajectories of equal radii.
Assertion : A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal.
Reason : Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field $\overrightarrow B $ in a direction perpendicular to $\overrightarrow B $, will describe circular trajectories of equal radii.
- [AIIMS 2009]
- A
If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
- B
If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
- C
If Assertion is correct but Reason is incorrect.
- D
If both the Assertion and Reason are incorrect.
Similar Questions
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
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
- [JEE MAIN 2022]
An electron is accelerated by a potential difference of $12000\, volts$. It then enters a uniform magnetic field of ${10^{ - 3}}\,T$ applied perpendicular to the path of electron. Find the radius of path. Given mass of electron $ = 9 \times {10^{ - 31}}\,kg$ and charge on electron $ = 1.6 \times {10^{ - 19}}\,C$
An electron is accelerated by a potential difference of $12000\, volts$. It then enters a uniform magnetic field of ${10^{ - 3}}\,T$ applied perpendicular to the path of electron. Find the radius of path. Given mass of electron $ = 9 \times {10^{ - 31}}\,kg$ and charge on electron $ = 1.6 \times {10^{ - 19}}\,C$
Answer the following questions:
$(a)$ A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
$(b)$ A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
$(c)$ An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.
Answer the following questions:
$(a)$ A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
$(b)$ A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
$(c)$ An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.
A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by
$\vec E = 2\hat i + 3\hat j ;\, B = 4\hat j + 6\hat k$
The charged particle is shifted from the origin to the point $P(x = 1 ;\, y = 1)$ along a straight path. The magnitude of the total work done is
A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by
$\vec E = 2\hat i + 3\hat j ;\, B = 4\hat j + 6\hat k$
The charged particle is shifted from the origin to the point $P(x = 1 ;\, y = 1)$ along a straight path. The magnitude of the total work done is
- [JEE MAIN 2019]
Consider the mass-spectrometer as shown in figure. The electric field between plates is $\vec E\ V/m$ , and the magnetic field in both the velocity selector and in the deflection chamber has magnitude $B$ . Find the radius $'r'$ for a singly charged ion of mass $'m'$ in the deflection chamber
Consider the mass-spectrometer as shown in figure. The electric field between plates is $\vec E\ V/m$ , and the magnetic field in both the velocity selector and in the deflection chamber has magnitude $B$ . Find the radius $'r'$ for a singly charged ion of mass $'m'$ in the deflection chamber