An alpha particle (charge +2 e ) and an Electron, ' & 60^∘ electron move in opposite directions

step 1 Both moving charges produce magnetic fields, and the net field is the vector sum of the two fiel

An alpha particle (charge +2 e ) and an Electron, ' & 60^∘...

An alpha particle (charge $+2 e$ ) and an Electron, ' $\& 60^{\circ}$ electron move in opposite directions from the same point, each with the speed of $2.80 \times 10^{5} \mathrm{~m} / \mathrm{s}$ (Fig. E28.4). Find the magnitude and direction of the total magnetic field these charges produce at point $P$, which is $1.80 \mathrm{nm}$ from each charge.

Key Concepts

Effect of Charge Sign on Magnetic Fields

The sign of the charge influences the direction of the magnetic field generated by a moving particle. While the magnitude is derived from the Biot-Savart law and depends on the absolute value of the charge, the direction is determined by the right-hand rule for positive charges and the opposite direction for negative charges. This distinction is key in problems involving particles of opposite charge moving in different directions.

Superposition Principle in Electromagnetism

In electromagnetic theory, the superposition principle states that the total magnetic field produced by multiple sources is the vector sum of the individual fields. This principle allows the separate calculation of the magnetic fields due to each moving charge, which are then added together to determine the net magnetic field at a given point.

Biot?Savart Law for Moving Charges

This law relates a moving electric charge to the magnetic field it produces. It states that a moving charge produces a magnetic field whose magnitude is proportional to the charge and its velocity and inversely proportional to the square of the distance from the charge. The direction of the field is given by the cross product of the velocity with the vector pointing from the charge to the field point, making it essential when calculating fields from moving particles.

Right?Hand Rule

The right?hand rule is a mnemonic used to determine the direction of the magnetic field produced by a positively charged particle in motion. When the thumb of the right hand points in the direction of the particle's velocity, the curl of the fingers shows the direction of the magnetic field loops around the path of the moving charge. For negatively charged particles, the direction is opposite, making it crucial for correctly assigning field directions.

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