In a H-atom, an electron moves in a circular orbit of radius 5.2 ×10^-11 meter and produces a ma

step 1 As we know that for a circular loop, B is equal to mu not i by 2a. So putting the value here, I

In a H-atom, an electron moves in a circular orbit of radius...

In a H-atom, an electron moves in a circular orbit of radius $5.2 \times 10^{-11}$ meter and produces a mag. field of $12.56$ Tesla at its nucleus. The current produced by the motion of the electron will be (a) $6.53 \times 10^{-3}$ (b) $13.25 \times 10^{-10}$ (c) $9.6 \times 10^{6}$ (d) $1.04 \times 10^{-3}$

In a H-atom, an electron moves in a circular orbit of radius $5.2 \times 10^{-11}$ meter and produces a mag. field of $12.56$ Tesla at its nucleus. The current produced by the motion of the electron will be
(a) $6.53 \times 10^{-3}$
(b) $13.25 \times 10^{-10}$
(c) $9.6 \times 10^{6}$
(d) $1.04 \times 10^{-3}$

Key Concepts

Orbital Period and Frequency

The orbital period is the time it takes for an electron to complete one full revolution around the nucleus. It is inversely related to the frequency of revolution, where a higher frequency corresponds to a shorter period. This relationship is critical in determining how the motion of the electron translates into an effective current, using the relation I = charge × frequency.

Magnetic Field from a Current Loop

A current loop generates a magnetic field at its center, and the magnitude of this field is directly related to the strength of the current and the geometry of the loop. In atomic models like the H-atom, the electron’s motion creates a magnetic dipole moment, and understanding this relationship is essential for linking the microscopic motion of electrons to macroscopic magnetic effects.

Electric Current in a Closed Loop

This concept refers to the definition of current as the amount of charge passing through a given point per unit time. In the context of an electron orbiting in a circular path, the current is calculated by taking the charge of the electron and dividing it by the period of its orbit. This foundational principle is essential in understanding how moving charges generate magnetic fields.

Circular Motion of Charged Particles

When a charged particle such as an electron moves in a circular orbit, it behaves like a current loop. The electron’s continuous motion along a closed path constitutes a steady current, which in turn gives rise to a magnetic field. This concept is pivotal in both classical electromagnetism and atomic physics to model the magnetic properties of atoms.

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