An electron follows a helical path in a uniform magnetic field of magnitude 1.30 T. The pitch o

An electron follows a helical path in a uniform magnetic...

Key Concepts

Magnetic Force on a Charged Particle

This concept involves the Lorentz force, which acts on a charged particle moving in a magnetic field. The force is given by the cross product F = q(v × B), meaning that it is always perpendicular to the particle's velocity. This perpendicular nature causes the particle’s trajectory to bend, leading to circular or curved motion rather than speeding it up or slowing it down directly.

Helical Motion in a Magnetic Field

When a charged particle has velocity components both perpendicular and parallel to a uniform magnetic field, its path becomes helical. The perpendicular component results in circular motion because of the magnetic force acting as a centripetal force, while the parallel component causes the particle to progress linearly along the direction of the magnetic field, combining to form a helical trajectory.

Centripetal Force in Circular Motion

In the context of a charged particle's motion in a magnetic field, the magnetic force acts as the centripetal force that keeps the particle in circular motion. This relationship is crucial for relating the speed of the particle to the radius of its circular path by equating the magnetic force to the required centripetal force (mv²/r).

Pitch of a Helical Path

The pitch of the helical path is the linear distance that a particle travels along the magnetic field direction during one complete rotation in the perpendicular plane. It provides a direct link between the linear (parallel) and rotational (perpendicular) components of the particle's motion and is useful in determining time-based characteristics of the motion, such as the period of rotation.

Cyclotron Frequency

The cyclotron frequency is the frequency with which a charged particle orbits in a circular path under the influence of a uniform magnetic field. It depends only on the charge and mass of the particle and the magnetic field strength, not on the speed of the particle. This concept is important in analyzing the dynamics of the circular component of the particle's helical motion.

Transcript

00:01 Hello student in this question if we see the language of the question then in this question we have given a heretical path in which electron is moving in a circular motion and moving also further you know that the helical path it's like same this type of moving this type so we are having this type of the path that this type of the path and these two values are given in the question that is the magnetic field that is 1 .3 tesla and the force when that electron is 2 to 2 multiplied by 10 raised to power minus 14 newton so in this question we have to take out the velocity of the electron so we know that the force the total force in this field the total force in this field is equal to q into electric field you multiply by electric field plus q that is charged multiply by velocity multiplied by magnetic field multiplied by sine theta sine theta is the angle between v and b so this formula is basically v cross b so this if we simplify this cross we get this side theta so after simplifying these values we know that the force is given in the position so putting these values and we know that in this portion there is no electric grid so this portion will be zero so final force will be q, v, b, sine theta.

01:37 Here, sine theta is 90 degree.

01:42 So its value is 1.

01:44 So here we get 1 value.

01:47 So after putting these values in this formula, we get 2 multiply by 10 raised to 4 minus 14 is equal to the charge on and electron equals to 1 .6 multiply by 10 x to 4 minus 19 electron and the velocity value we have to find so multiply by velocity and the value of magnetic field that is given in the that is 1 .3 tesla so after rearranging these formula we get velocity equals to 2 multiply by 10 raise to power minus 14 divided by 1 .6 multiplied by 10 x multiplied by 10 and raised to 4 minus 19 multiplied by 1 .3...

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