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Questions and Answers
What are the two types of fields used in the cyclotron?
What do the semicircular containers in a cyclotron resemble?
How does the frequency of revolution of a charged particle in a magnetic field change with its energy?
What happens to the charged particle when it transitions from one dee to another?
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What is the primary function of the electric field within a cyclotron?
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What is the effect of the magnetic field on a charged particle in the cyclotron?
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What is increased each time the particle accelerates in the cyclotron?
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Why is the cyclotron considered efficient for acceleration?
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Under what condition will a charged particle describe a circular path in a magnetic field?
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What remains unchanged when a charged particle has a component of velocity along the magnetic field B?
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If the radius of a circular path of a particle is represented by r, which formula represents the relationship between radius and particle parameters?
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What does the angular frequency ω depend on for a charged particle in a magnetic field?
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How is the frequency (ν) of rotation related to the energy of the charged particle?
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What is the expression for the centripetal force acting on a charged particle in circular motion?
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What is the significance of the radius of the circular path relating to momentum?
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What does T represent in the motion of a charged particle in a magnetic field?
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What physical role does the electric field E have?
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According to the equation $F = q E$, what does F represent?
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What fundamental concept did Faraday contribute to the study of electric fields?
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In the expression for electric field $E = Q rac{ ext{r̂}}{4 ext{πε}_0 r^2}$, what does $ ext{r̂}$ represent?
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What assumption is made regarding the electric fields in the discussed chapter?
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Where does the origin of the electric field, in a physical sense, come from?
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What is indicated by the term $ ext{πε}_0$ in the electric field equation?
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What happens to the electric field as the distance r increases, according to the formula $E = Q rac{ ext{r̂}}{4 ext{πε}_0 r^2}$?
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What type of accelerator was established at the Saha Institute of Nuclear Physics in 1953?
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Which of the following institutions built a 5.5 MV Van de Graaff accelerator in 1963?
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What was built indigenously in Kolkata during the seventies and eighties?
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Which facility is responsible for the installation of a 14 MV Tandem Pelletron accelerator?
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Where is a 2 GeV Synchrotron Radiation Source being constructed?
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What type of accelerator system is the Department of Atomic Energy considering for future applications?
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What major addition are TIFR and IUAC making to their facilities?
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Which university was the recipient of a 66 cm Cyclotron donated by Rochester University?
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What is the relationship between the magnetic field element dB and the displacement vector r?
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Why do the components of dB perpendicular to the x-axis cancel out?
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What does the net magnetic field B at point P depend on?
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What does the equation dBx = dB cos θ represent?
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Considering the integral for dB, what is the result when summing the contributions over a complete loop?
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What is the significance of the term µ0 in the magnetic field equations?
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What remains at the center of the circular loop based on the derived magnetic field equation?
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How is the angle θ calculated in relation to the components of the magnetic field?
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Study Notes
Electric and Magnetic Fields
- The electric field (E) at a point due to a charge Q is described by Coulomb's law: E = Qr̂ / (4πε0)r2.
- The force F experienced by a charge q in an electric field is given by: F = qE.
- The concept of fields was first introduced by Faraday and later incorporated by Maxwell's unification of electricity and magnetism.
- The magnetic field acts perpendicular to both the velocity and the magnetic field, behaving like a centripetal force.
- The radius of the circular path of a charged particle in a magnetic field is given by: r = mv/qB (where m is mass, v is velocity, q is charge, and B is magnetic field)
Circular and Helical Motion in Magnetic Fields
- A charged particle moving in a uniform magnetic field will follow a circular path if the velocity (v) and magnetic field (B) are perpendicular.
- The angular frequency (ω) of this circular motion is given by: ω = 2πν = qB/m (independent of the velocity or energy).
- If the velocity has a component along the magnetic field, the particle will follow a helical path.
Cyclotrons
- Cyclotrons utilize both electric and magnetic fields to accelerate charged particles.
- The frequency of revolution of a charged particle in a magnetic field is independent of its energy, which is a key principle in cyclotron design.
- Cyclotrons use two semicircular, metal containers called "dees" where particles are shielded from the electric field but are acted upon by the magnetic field.
- The electric field between the dees alternates in tune with the particle's motion, accelerating the particle each time it moves between the dees.
Magnetic Field Due to a Circular Loop
- The magnetic field at a point P on the axis of a circular loop carrying current I is given by: B = (µ0IR2) / (2(x2 + R2)3/2) ˆi.
- The field at the centre of the loop can be obtained as a special case of this result.
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Description
Explore the fundamental principles of electric and magnetic fields. This quiz covers Coulomb's law, force on charges, Faraday's concepts, and the motion of charged particles in magnetic fields. Test your understanding of these essential physics concepts.
