A proton moves at 2.50 ×10^6 m / s horizontally at a right angle to a magnetic field. a. What is

step 1 A proton moves horizontally at a right angle to a magnetic field. Part A is what is the strength

A proton moves at 2.50 ×10^6 m / s horizontally at a right...

A proton moves at $2.50 \times 10^{6} \mathrm{m} / \mathrm{s}$ horizontally at a right angle to a magnetic field. a. What is the strength of the magnetic field required to exactly balance the weight of the proton and keep it moving horizontally! b. Should the direction of the magnetic field be in a horizontal or a vertical plane?

A proton moves at $2.50 \times 10^{6} \mathrm{m} / \mathrm{s}$ horizontally at a right angle to a magnetic field.
a. What is the strength of the magnetic field required to exactly balance the weight of the proton and keep it moving horizontally!
b. Should the direction of the magnetic field be in a horizontal or a vertical plane?

Key Concepts

Right-Hand Rule

The right-hand rule is a mnemonic used in physics to determine the direction of the magnetic force on a moving charge. By pointing the thumb in the direction of the charge’s velocity and the fingers in the direction of the magnetic field, the magnetic force is indicated by the direction in which the palm faces. This rule assists in visualizing and predicting the orientation of the forces in three-dimensional space, which is essential for setting up the correct field orientation to achieve force balance.

Magnetic Force on Moving Charges

The magnetic force acting on a charged particle moving in a magnetic field is given by the Lorentz force law, expressed as F = qvB sin(?), where q is the charge, v is the speed of the particle, B is the magnetic field strength, and ? is the angle between the velocity and the magnetic field. When the motion is perpendicular to the magnetic field, sin(?) equals 1, simplifying the calculation of the force. This force is always perpendicular to both the velocity of the particle and the magnetic field direction.

Gravitational Force

Gravitational force, commonly referred to as weight, is the force with which a mass is attracted towards the Earth. It is calculated as F = mg, where m is the mass of the object and g is the acceleration due to gravity. In problems where magnetic forces are used to counteract gravity, equating the magnetic force to the gravitational force allows one to solve for the necessary magnetic field strength.

Equilibrium of Forces

Establishing equilibrium between different forces means setting the net force acting on an object to zero. In scenarios where a magnetic force is used to balance the gravitational force, the magnitude of the magnetic force is set equal to the force of gravity. This equilibrium condition is crucial for maintaining a constant velocity and position, ensuring that the particle moves with a uniform horizontal trajectory while its weight is counterbalanced.

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