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Charge q and mass M is initially at rest at origin electric field is given by the north check ab while magnetic field is B not K cap find speed of particle when coordinator of particle are?
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**Electric Field and Magnetic Field**
The given problem involves a charged particle with charge q and mass M that is initially at rest at the origin. The electric field is given as E = E_0 î + E_1 ĵ, and the magnetic field is given as B = B_0 k̂.
**Dynamics of the Charged Particle**
To determine the speed of the particle at a given position, we need to consider the forces acting on the particle. The Lorentz force on a charged particle moving in an electric field and magnetic field is given by the equation:
F = q(E + v × B)
where F is the net force, q is the charge of the particle, E is the electric field, v is the velocity vector of the particle, and B is the magnetic field.
**Analyzing the Forces**
In this case, the particle is initially at rest, so its velocity vector v is zero. Therefore, the net force acting on the particle is only due to the electric field:
F = qE
Since the force is directly proportional to the electric field, the direction of the force is in the same direction as the electric field vector. In this case, the force is given by:
F = q(E_0 î + E_1 ĵ)
**Determining the Acceleration**
To determine the acceleration of the particle, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = ma
Substituting the force equation into Newton's second law, we have:
q(E_0 î + E_1 ĵ) = ma
**Finding the Speed of the Particle**
To find the speed of the particle at a given position, we need to integrate the acceleration equation with respect to time. However, since the particle starts from rest, its initial velocity is zero. Therefore, the velocity of the particle at any given time t can be expressed as:
v = ∫(q(E_0 î + E_1 ĵ)/m) dt
Integrating the equation, we obtain:
v = (q/m)(E_0 î + E_1 ĵ)t + v_0
where v_0 is the initial velocity of the particle (which is zero in this case). Hence, the speed of the particle at any given time t is given by:
|v| = |(q/m)(E_0 î + E_1 ĵ)t|
This equation gives us the speed of the particle at any given time t, based on the given electric field and magnetic field.
The given problem involves a charged particle with charge q and mass M that is initially at rest at the origin. The electric field is given as E = E_0 î + E_1 ĵ, and the magnetic field is given as B = B_0 k̂.
**Dynamics of the Charged Particle**
To determine the speed of the particle at a given position, we need to consider the forces acting on the particle. The Lorentz force on a charged particle moving in an electric field and magnetic field is given by the equation:
F = q(E + v × B)
where F is the net force, q is the charge of the particle, E is the electric field, v is the velocity vector of the particle, and B is the magnetic field.
**Analyzing the Forces**
In this case, the particle is initially at rest, so its velocity vector v is zero. Therefore, the net force acting on the particle is only due to the electric field:
F = qE
Since the force is directly proportional to the electric field, the direction of the force is in the same direction as the electric field vector. In this case, the force is given by:
F = q(E_0 î + E_1 ĵ)
**Determining the Acceleration**
To determine the acceleration of the particle, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = ma
Substituting the force equation into Newton's second law, we have:
q(E_0 î + E_1 ĵ) = ma
**Finding the Speed of the Particle**
To find the speed of the particle at a given position, we need to integrate the acceleration equation with respect to time. However, since the particle starts from rest, its initial velocity is zero. Therefore, the velocity of the particle at any given time t can be expressed as:
v = ∫(q(E_0 î + E_1 ĵ)/m) dt
Integrating the equation, we obtain:
v = (q/m)(E_0 î + E_1 ĵ)t + v_0
where v_0 is the initial velocity of the particle (which is zero in this case). Hence, the speed of the particle at any given time t is given by:
|v| = |(q/m)(E_0 î + E_1 ĵ)t|
This equation gives us the speed of the particle at any given time t, based on the given electric field and magnetic field.
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Charge q and mass M is initially at rest at origin electric field is given by the north check ab while magnetic field is B not K cap find speed of particle when coordinator of particle are?
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Charge q and mass M is initially at rest at origin electric field is given by the north check ab while magnetic field is B not K cap find speed of particle when coordinator of particle are? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Charge q and mass M is initially at rest at origin electric field is given by the north check ab while magnetic field is B not K cap find speed of particle when coordinator of particle are? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Charge q and mass M is initially at rest at origin electric field is given by the north check ab while magnetic field is B not K cap find speed of particle when coordinator of particle are?.
Charge q and mass M is initially at rest at origin electric field is given by the north check ab while magnetic field is B not K cap find speed of particle when coordinator of particle are? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Charge q and mass M is initially at rest at origin electric field is given by the north check ab while magnetic field is B not K cap find speed of particle when coordinator of particle are? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Charge q and mass M is initially at rest at origin electric field is given by the north check ab while magnetic field is B not K cap find speed of particle when coordinator of particle are?.
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