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In a region of space that extends from x= 0 to x=L a uniform magnetic field B is directed along negative z axis . A charged particle is projected with velocity Vnot at X=0 along positive x axis the particle emerges at x =L after suffering a deviation of 60°.the velocity with which same particle is projected at X=0 along positive X axis so that when it emerges at X=L the deviation sufferd by it is 30°is
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Explanation of the problem:
A charged particle is projected with velocity Vnot at x=0 along the positive x-axis. The particle emerges at x=L after suffering a deviation of 60°. The magnetic field B is uniform and directed along the negative z-axis. We need to find the velocity with which the same particle is projected at x=0 along the positive x-axis so that when it emerges at x=L, the deviation suffered by it is 30°.
Solution:
1. Calculation of initial velocity:
We know that the magnetic force on a charged particle moving in a magnetic field is given by:
F = q (v x B)
Where,
F = Magnetic force
q = Charge of the particle
v = Velocity of the particle
B = Magnetic field
Since the magnetic force is perpendicular to the velocity of the particle, it causes the particle to move in a circular path. The radius of this circular path can be calculated using the formula:
r = (mv) / (qB)
Where,
m = Mass of the particle
When the particle is projected with the velocity Vnot along the positive x-axis, it experiences a magnetic force towards the negative y-axis. This force causes the particle to move in a circular path. Due to the circular motion, the particle emerges at x=L after suffering a deviation of 60°. Using the above formula, we can calculate the radius of the circular path as:
r = (mVnot) / (qB)
Since the particle emerges at x=L after suffering a deviation of 60°, it means that the particle has covered an arc length of 60° on the circular path. Using the formula for arc length, we can calculate the circumference of the circular path as:
C = 2πr (60/360)
Substituting the value of r, we get:
C = (2πmVnot) / (qB) (1/6)
The time taken by the particle to cover this arc length can be calculated as:
t = (arc length) / (velocity)
Substituting the values, we get:
t = (L/6) / Vnot
Since the particle is moving in a circular path, the centripetal force acting on it is given by:
F = mv^2 / r
Substituting the value of r, we get:
F = (mqBVnot) / mVnot
Simplifying, we get:
F = qBVnot
Equating this force with the magnetic force, we get:
qBVnot = qB (radians per second) (r)
Substituting the values, we get:
qBVnot = qB (2π/6t) (L/2π)
Simplifying, we get:
Vnot = (L/6t)
2. Calculation of final velocity:
When the same particle is projected with the velocity V along the positive x-axis, it experiences a magnetic force towards the negative y-axis. This force causes the particle to move in a circular path. Due to the circular motion, the particle emerges at x=L after suffering a deviation of 30°. Using the above formula, we can calculate the radius of the circular path as:
r = (mV) / (qB)
Since the particle emerges
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In a region of space that extends from x= 0 to x=L a uniform magnetic field B is directed along negative z axis . A charged particle is projected with velocity Vnot at X=0 along positive x axis the particle emerges at x =L after suffering a deviation of 60°.the velocity with which same particle is projected at X=0 along positive X axis so that when it emerges at X=L the deviation sufferd by it is 30°is
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In a region of space that extends from x= 0 to x=L a uniform magnetic field B is directed along negative z axis . A charged particle is projected with velocity Vnot at X=0 along positive x axis the particle emerges at x =L after suffering a deviation of 60°.the velocity with which same particle is projected at X=0 along positive X axis so that when it emerges at X=L the deviation sufferd by it is 30°is for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about In a region of space that extends from x= 0 to x=L a uniform magnetic field B is directed along negative z axis . A charged particle is projected with velocity Vnot at X=0 along positive x axis the particle emerges at x =L after suffering a deviation of 60°.the velocity with which same particle is projected at X=0 along positive X axis so that when it emerges at X=L the deviation sufferd by it is 30°is covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a region of space that extends from x= 0 to x=L a uniform magnetic field B is directed along negative z axis . A charged particle is projected with velocity Vnot at X=0 along positive x axis the particle emerges at x =L after suffering a deviation of 60°.the velocity with which same particle is projected at X=0 along positive X axis so that when it emerges at X=L the deviation sufferd by it is 30°is.
In a region of space that extends from x= 0 to x=L a uniform magnetic field B is directed along negative z axis . A charged particle is projected with velocity Vnot at X=0 along positive x axis the particle emerges at x =L after suffering a deviation of 60°.the velocity with which same particle is projected at X=0 along positive X axis so that when it emerges at X=L the deviation sufferd by it is 30°is for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about In a region of space that extends from x= 0 to x=L a uniform magnetic field B is directed along negative z axis . A charged particle is projected with velocity Vnot at X=0 along positive x axis the particle emerges at x =L after suffering a deviation of 60°.the velocity with which same particle is projected at X=0 along positive X axis so that when it emerges at X=L the deviation sufferd by it is 30°is covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a region of space that extends from x= 0 to x=L a uniform magnetic field B is directed along negative z axis . A charged particle is projected with velocity Vnot at X=0 along positive x axis the particle emerges at x =L after suffering a deviation of 60°.the velocity with which same particle is projected at X=0 along positive X axis so that when it emerges at X=L the deviation sufferd by it is 30°is.
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