Kieran measures the magnetic field of an electron beam. The...

Kieran measures the magnetic field of an electron beam. The beam strength is such that $1.40 \times 10^{11}$ electrons pass a point every $1.30 \mu$ s. What magnetic field does Kieran measure at a distance of $2.00 \mathrm{cm}$ from the beam center?

Key Concepts

Elementary Charge

The elementary charge is the smallest unit of electric charge observed in nature, with an approximate value of 1.602 × 10?¹? coulombs. It is the charge carried by a single proton (or the negative of that for an electron). This constant is critical when converting a count of charged particles, such as electrons in an electron beam, into the total charge driving the current.

Magnetic Field from a Current-Carrying Conductor

A fundamental concept in electromagnetism is that a moving charge, or a current, produces a magnetic field. For a long, straight conductor, the magnetic field at a distance from the wire can be calculated using the formula B = (??I) / (2?r), where ?? is the permeability of free space, I is the current, and r is the radial distance from the wire. This relation is derived from Ampère’s law and is essential for understanding magnetic fields generated by currents.

Electric Current

Electric current is defined as the amount of electric charge that passes a point per unit time. In physics, it is usually measured in amperes (A), where one ampere corresponds to one coulomb of charge per second. When dealing with moving charges, such as electrons in a beam, the current is obtained by multiplying the number of electrons by the elementary charge and then dividing by the time interval during which these electrons pass a given point.

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