What Is The Magnetic Force On A Proton Moving At $5.2 \times 10^7 \, \text{m/s}$ To The Left Through A Magnetic Field Of $2.4 \, \text{T}$ Pointing Toward You? The Charge On A Proton Is $1.6 \times 10^{-19} \, \text{C}$. Use

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Introduction

The magnetic force on a moving charge is a fundamental concept in physics, governed by the Lorentz force equation. This equation describes the force experienced by a charge moving through a magnetic field. In this article, we will explore the magnetic force on a proton moving at a specific velocity through a magnetic field of a given strength.

The Lorentz Force Equation

The Lorentz force equation is a fundamental concept in physics that describes the force experienced by a charge moving through a magnetic field. The equation is given by:

F=q(E+v×B){ \mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B}) }

where F\mathbf{F} is the force experienced by the charge, qq is the charge of the particle, E\mathbf{E} is the electric field, v\mathbf{v} is the velocity of the particle, and B\mathbf{B} is the magnetic field.

Magnetic Force on a Moving Charge

The magnetic force on a moving charge is given by the cross product of the velocity and magnetic field vectors. This force is perpendicular to both the velocity and magnetic field vectors. The magnitude of the magnetic force is given by:

F=qvBsin⁡θ{ F = qvB \sin \theta }

where θ\theta is the angle between the velocity and magnetic field vectors.

Given Values

In this problem, we are given the following values:

  • The velocity of the proton is 5.2×107 m/s5.2 \times 10^7 \, \text{m/s}.
  • The magnetic field strength is 2.4 T2.4 \, \text{T}.
  • The charge on a proton is 1.6×10−19 C1.6 \times 10^{-19} \, \text{C}.

Calculating the Magnetic Force

To calculate the magnetic force on the proton, we need to substitute the given values into the equation for the magnetic force.

First, we need to determine the angle between the velocity and magnetic field vectors. Since the magnetic field is pointing toward us and the proton is moving to the left, the angle between the velocity and magnetic field vectors is 180∘180^\circ. Therefore, sin⁡θ=1\sin \theta = 1.

Next, we can substitute the given values into the equation for the magnetic force:

F=qvBsin⁡θ{ F = qvB \sin \theta }

F=(1.6×10−19 C)(5.2×107 m/s)(2.4 T)(1){ F = (1.6 \times 10^{-19} \, \text{C})(5.2 \times 10^7 \, \text{m/s})(2.4 \, \text{T})(1) }

F=1.9328×10−11 N{ F = 1.9328 \times 10^{-11} \, \text{N} }

Conclusion

In this article, we have calculated the magnetic force on a proton moving at 5.2×107 m/s5.2 \times 10^7 \, \text{m/s} to the left through a magnetic field of 2.4 T2.4 \, \text{T} pointing toward us. The charge on a proton is 1.6×10−19 C1.6 \times 10^{-19} \, \text{C}. We have used the Lorentz force equation to calculate the magnetic force, and have found that the force is 1.9328×10−11 N1.9328 \times 10^{-11} \, \text{N}.

Discussion

The magnetic force on a moving charge is a fundamental concept in physics, and is governed by the Lorentz force equation. This equation describes the force experienced by a charge moving through a magnetic field. In this article, we have calculated the magnetic force on a proton moving at a specific velocity through a magnetic field of a given strength.

The magnetic force on a moving charge is perpendicular to both the velocity and magnetic field vectors. The magnitude of the magnetic force is given by the equation F=qvBsin⁡θF = qvB \sin \theta, where θ\theta is the angle between the velocity and magnetic field vectors.

In this problem, we have assumed that the angle between the velocity and magnetic field vectors is 180∘180^\circ. This is because the magnetic field is pointing toward us and the proton is moving to the left. Therefore, sin⁡θ=1\sin \theta = 1.

The magnetic force on a moving charge is an important concept in physics, and has many practical applications. For example, it is used in the design of particle accelerators, where charged particles are accelerated to high speeds and then steered through magnetic fields to produce a desired trajectory.

Applications

The magnetic force on a moving charge has many practical applications in physics and engineering. Some examples include:

  • Particle accelerators: The magnetic force on a moving charge is used to steer charged particles through magnetic fields to produce a desired trajectory.
  • Magnetic resonance imaging (MRI): The magnetic force on a moving charge is used to create images of the body by manipulating the magnetic field and detecting the signals produced by the moving charges.
  • Electric motors: The magnetic force on a moving charge is used to produce torque in electric motors.
  • Magnetic brakes: The magnetic force on a moving charge is used to create magnetic brakes, which can be used to slow down or stop moving objects.

Conclusion

In conclusion, the magnetic force on a moving charge is a fundamental concept in physics, governed by the Lorentz force equation. This equation describes the force experienced by a charge moving through a magnetic field. In this article, we have calculated the magnetic force on a proton moving at 5.2×107 m/s5.2 \times 10^7 \, \text{m/s} to the left through a magnetic field of 2.4 T2.4 \, \text{T} pointing toward us. The charge on a proton is 1.6×10−19 C1.6 \times 10^{-19} \, \text{C}. We have used the Lorentz force equation to calculate the magnetic force, and have found that the force is 1.9328×10−11 N1.9328 \times 10^{-11} \, \text{N}.

The magnetic force on a moving charge has many practical applications in physics and engineering, including particle accelerators, magnetic resonance imaging (MRI), electric motors, and magnetic brakes.

Introduction

In our previous article, we calculated the magnetic force on a proton moving at 5.2×107 m/s5.2 \times 10^7 \, \text{m/s} to the left through a magnetic field of 2.4 T2.4 \, \text{T} pointing toward us. The charge on a proton is 1.6×10−19 C1.6 \times 10^{-19} \, \text{C}. In this article, we will answer some frequently asked questions about the magnetic force on a moving charge.

Q: What is the magnetic force on a moving charge?

A: The magnetic force on a moving charge is a fundamental concept in physics, governed by the Lorentz force equation. This equation describes the force experienced by a charge moving through a magnetic field.

Q: What is the Lorentz force equation?

A: The Lorentz force equation is given by:

F=q(E+v×B){ \mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B}) }

where F\mathbf{F} is the force experienced by the charge, qq is the charge of the particle, E\mathbf{E} is the electric field, v\mathbf{v} is the velocity of the particle, and B\mathbf{B} is the magnetic field.

Q: What is the magnitude of the magnetic force?

A: The magnitude of the magnetic force is given by:

F=qvBsin⁡θ{ F = qvB \sin \theta }

where θ\theta is the angle between the velocity and magnetic field vectors.

Q: What is the direction of the magnetic force?

A: The direction of the magnetic force is perpendicular to both the velocity and magnetic field vectors.

Q: What is the unit of the magnetic force?

A: The unit of the magnetic force is Newtons (N).

Q: What are some practical applications of the magnetic force on a moving charge?

A: Some practical applications of the magnetic force on a moving charge include:

  • Particle accelerators: The magnetic force on a moving charge is used to steer charged particles through magnetic fields to produce a desired trajectory.
  • Magnetic resonance imaging (MRI): The magnetic force on a moving charge is used to create images of the body by manipulating the magnetic field and detecting the signals produced by the moving charges.
  • Electric motors: The magnetic force on a moving charge is used to produce torque in electric motors.
  • Magnetic brakes: The magnetic force on a moving charge is used to create magnetic brakes, which can be used to slow down or stop moving objects.

Q: What is the relationship between the magnetic force and the electric field?

A: The magnetic force on a moving charge is independent of the electric field. The Lorentz force equation shows that the force experienced by a charge moving through a magnetic field is given by:

F=q(E+v×B){ \mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B}) }

This means that the magnetic force on a moving charge is given by the cross product of the velocity and magnetic field vectors, and is independent of the electric field.

Q: What is the relationship between the magnetic force and the velocity of the charge?

A: The magnetic force on a moving charge is proportional to the velocity of the charge. The magnitude of the magnetic force is given by:

F=qvBsin⁡θ{ F = qvB \sin \theta }

This means that the magnetic force on a moving charge increases with the velocity of the charge.

Q: What is the relationship between the magnetic force and the magnetic field strength?

A: The magnetic force on a moving charge is proportional to the magnetic field strength. The magnitude of the magnetic force is given by:

F=qvBsin⁡θ{ F = qvB \sin \theta }

This means that the magnetic force on a moving charge increases with the magnetic field strength.

Conclusion

In conclusion, the magnetic force on a moving charge is a fundamental concept in physics, governed by the Lorentz force equation. This equation describes the force experienced by a charge moving through a magnetic field. We have answered some frequently asked questions about the magnetic force on a moving charge, including the magnitude, direction, and unit of the magnetic force, as well as some practical applications of the magnetic force on a moving charge.