An electron moves in a circular orbit with a uniform speed v. It produces a magnetic field B at the centre of the circle. The radius of the circle is proportional to:
\(\frac{B}{v}\)
\(\frac{v}{B}\)
\(\sqrt{\bigg(\frac{v}{B}\bigg)}\)
\(\sqrt{\bigg(\frac{B}{v}\bigg)}\)
The Correct Option is C
Solution and Explanation
Centripetal force is provided by magnetic force.
Fcentripetal = Fmagnetic
∴\(\frac{mv^2}{r}\) =qvB
r = \(\frac{mv}{qb}\)
\(\Rightarrow\) r \(\propto \, \frac{v}{B}\)
since\(\frac{m}{q}\) is constant
Correct option is (C): \(\sqrt{\bigg(\frac{v}{B}\bigg)}\)
Top Questions on kinetic theory
- In a mixture of gases, the average number of degrees of freedom per molecule is 6. If the rms speed of the molecule is \(c\), what is the velocity of sound in the gas?
- BITSAT - 2025
- Physics
- kinetic theory
- Mean free path is inversely proportional to (n = number density, d = diameter of particle)
- KEAM - 2025
- Physics
- kinetic theory
- The equation for the RMS velocity is given as \[ v_{\text{rms}} = \sqrt{\frac{3RT}{M_0}} \] where \( R \) is the gas constant, \( T \) is the temperature, and \( M_0 \) is the molecular mass. If the temperature is increased, find the new RMS velocity \( v_{\text{rms}} \) when the temperature is doubled.}
- MHT CET - 2025
- Physics
- kinetic theory
The motion of a particle in the XY plane is given by \( x(t) = 25 + 6t^2 \, \text{m} \); \( y(t) = -50 - 20t + 8t^2 \, \text{m} \). The magnitude of the initial velocity of the particle, \( v_0 \), is given by:
- OJEE - 2024
- Physics
- kinetic theory
- A body of mass \( m \) moves along the X-axis such that at time \( t \), its position is \( x(t) = \alpha t^4 - \beta t^3 + \gamma t \), where \( \alpha \), \( \beta \), and \( \gamma \) are constants. The acceleration of the body is:
- OJEE - 2024
- Physics
- kinetic theory
Questions Asked in NEET exam
The current passing through the battery in the given circuit, is:
- NEET (UG) - 2025
- Current electricity
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :
- NEET (UG) - 2025
- Pendulums
- Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y. She notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.
- NEET (UG) - 2025
- Relative Velocity
- The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at \(22.5^\circ\) from the polarization axis of one of the polaroids (\(I_0\) is the intensity of polarised light after passing through the first polaroid):
- NEET (UG) - 2025
- Polarization
A full wave rectifier circuit with diodes (\(D_1\)) and (\(D_2\)) is shown in the figure. If input supply voltage \(V_{in} = 220 \sin(100 \pi t)\) volt, then at \(t = 15\) msec:
- NEET (UG) - 2025
- Semiconductor Diode
Concepts Used:
Kinetic Theory
The kinetic theory is a fundamental concept in physics and chemistry that describes the behavior of gases, liquids, and solids in terms of the motion of their constituent particles. According to the kinetic theory, all matter is made up of tiny particles, such as atoms or molecules, that are constantly in motion.
The kinetic theory postulates that the temperature of a substance is directly proportional to the average kinetic energy of its particles. The higher the temperature, the greater the motion of the particles, and the more energy they possess.
In a gas, the kinetic theory explains that the particles move randomly and independently, colliding with one another and with the walls of their container. These collisions are elastic which means that no energy has lost during the collision. As a result, the pressure of the gas is directly related to the average speed of its particles and the number of collisions per unit area.
In a liquid or a solid, the particles are more closely packed and have less freedom of motion than in a gas. However, they still vibrate and move, and the kinetic theory explains their behavior in terms of the strength of their intermolecular forces and the amount of energy they possess.
Overall, the kinetic theory provides a framework for understanding the behavior of matter at the atomic and molecular level and has many practical applications, such as in the design of engines, the production of gases, and the study of the properties of materials.