What is the period of revolution for a charged particle in a magnetic field?

In summary, the Motor Principle is a fundamental law of electromagnetism that explains the relationship between electricity and magnetism in motors. It is applied in electric motors by using the force exerted on a wire in a magnetic field to create rotational motion. This principle has numerous real-world applications, such as in household appliances, vehicles, and medical equipment. It is closely related to other principles in electromagnetism and has evolved significantly since its discovery, leading to advancements in technology and the development of more efficient electric motors.
  • #1
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A charged particle with a charge-to-mass ratio of 5.7x10^8 C/Kg travels in a magnetic field of strength 0.75T in a circular path that's perpendicular to the magnetic field. What is the period of revolution for this particle.
 
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  • #2
The magnetic force exerted provides the centripetal force required to keep it in a circular path.
Do you know an equation for the magnetic force exerted on a charge,Q,moving with a velocity,v, in a magnetic field of flux density,B?
Do you know an equation for centripetal force??
 
  • #3


I would approach this question by first understanding the principles involved. The Motor Principle, also known as the Lorentz force law, states that when a charged particle moves in a magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field. This force causes the particle to move in a circular path.

In this scenario, we are given the charge-to-mass ratio of the particle, its velocity, and the strength of the magnetic field. Using the Motor Principle, we can calculate the force acting on the particle by multiplying its charge-to-mass ratio by the velocity and the strength of the magnetic field. This force is equal to the centripetal force required to keep the particle moving in a circular path.

We can then use the formula for centripetal force, F = mv²/r, where m is the mass of the particle, v is its velocity, and r is the radius of the circular path. Since we are given the charge-to-mass ratio of the particle, we can rearrange the formula to solve for the radius, r = mv/ (qB), where q is the charge of the particle and B is the magnetic field strength.

Now, we can use the formula for the period of revolution, T = 2πr/v, to calculate the time it takes for the particle to complete one full revolution in its circular path. Substituting the value of r we calculated earlier, we get T = 2π (mv/qB)/v = 2πm/qB.

Plugging in the given values, we get T = 2π (5.7x10^8 C/Kg)(0.75 T) = 2.7x10^-6 seconds.

Therefore, the period of revolution for this particle is 2.7x10^-6 seconds. This means that the particle completes one full revolution in its circular path every 2.7 microseconds. This calculation is important for understanding the behavior of charged particles in magnetic fields and can have practical applications in fields such as particle physics and electromagnetism.
 

1. What is the Motor Principle?

The Motor Principle is a fundamental law of electromagnetism that describes the relationship between electricity and magnetism in a motor. It states that when an electric current is passed through a wire in the presence of a magnetic field, a force is exerted on the wire that causes it to move. This is the basic principle behind the operation of electric motors.

2. How is the Motor Principle applied in electric motors?

The Motor Principle is applied in electric motors by using the force exerted on a wire in a magnetic field to create rotational motion. This is achieved by placing a wire coil, called an armature, in between the poles of a permanent magnet. When an electric current is passed through the armature, it experiences a force that causes it to rotate, thus creating the motion needed for the motor to function.

3. What are some real-world applications of the Motor Principle?

The Motor Principle has numerous real-world applications, the most common being electric motors used in household appliances, vehicles, and industrial machinery. It is also used in generators to convert mechanical energy into electrical energy. Additionally, the principle is applied in medical equipment such as MRI machines and in various other electromechanical devices.

4. How does the Motor Principle relate to other principles in electromagnetism?

The Motor Principle is closely related to other principles in electromagnetism, such as Faraday's Law of Induction and Lenz's Law. It is also a key component in the operation of generators, which use the opposite relationship of converting mechanical energy into electrical energy. The Motor Principle is also related to the Lorentz Force Law, which describes the force exerted on a charged particle moving in a magnetic field.

5. How has the Motor Principle evolved over time?

The Motor Principle has evolved significantly since its discovery in the early 19th century. It was first described by physicist Hans Christian Oersted in 1820 and has since been refined and expanded upon by scientists such as Michael Faraday and James Clerk Maxwell. With advancements in technology, the Motor Principle has been applied in new and innovative ways, leading to the development of more efficient and powerful electric motors.

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