Q. 385.0( 1 Vote )

A particle of mass m and positive charge q, moving with a uniform velocity v, enters a magnetic field B as shown in figure.

(a) Find the radius of the circular arc it describes in the magnetic field.

(b) Find the angle subtended by the arc at the centre.

(c) How long does the particle stay inside the magnetic field?

(d) Solve the three parts on the above problem if the charge q on the particle is negative.



Answer :


Given-
Mass of the particle = m
Positive charge on the particle = q
velocity of the particle = v
Magnetic field = B


(a)The radius of the circular arc described by the particle in the magnetic field-


We know,


The radius of the circle is given by,



where,


m is the mass of a proton


v= velocity of the particle


B = magnetic force


q= charge on the particle = C


(b) The angle subtended by the arc at the centre



Line MAB is the tangent to arc ABC,


When the particle enters into the magnetic field, it follows a path in the form of arc as shown in fig.


Now, the angle described by the charged particle is nothing but the angle MAO is ,



MAO = 90°



Also from fig ,
NAC = 90°



OAC = OCA = θ
Then, by angle-sum property of a triangle, sum of all angles of a triangle is 1800


AOC =180°− (θ + θ)


=


(c)The time for which the particle stay inside the magnetic field is given by-


Distance covered by the particle inside the magnetic field,is the length of arc subtended by angle θ and the radius



l = rθ


from (1)



l= r


time taken for a complete cycle will be its circumference and


the velocity is V -



Also The radius of the circle is given by,



where,


m is the mass of a proton


v= velocity of the particle


B = magnetic force


q= charge on the particle = C



(d) If the charge q on the particle is negative, then



(i) Radius of circular arc is given by



(ii) The centre of the arc lies within the magnetic field


Therefore, the angle subtended by the arc =



(iii) The time taken by the particle to cover the path inside the magnetic field



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Equation of electric and magnetic fieldEquation of electric and magnetic fieldEquation of electric and magnetic field52 mins
Magnetic force on moving charge particle in magnetic field | QuizMagnetic force on moving charge particle in magnetic field | QuizMagnetic force on moving charge particle in magnetic field | Quiz32 mins
Magnetic force on moving charge particle in magnetic fieldMagnetic force on moving charge particle in magnetic fieldMagnetic force on moving charge particle in magnetic field44 mins
Magnetic field due to current carrying straight wireMagnetic field due to current carrying straight wireMagnetic field due to current carrying straight wire37 mins
Magnetic field due to current carrying circular loopMagnetic field due to current carrying circular loopMagnetic field due to current carrying circular loop36 mins
Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)47 mins
Few Applications of Gauss's lawFew Applications of Gauss's lawFew Applications of Gauss's law54 mins
Electric field inside cavityElectric field inside cavityElectric field inside cavity37 mins
Gain Confidence on Magnetic Effects of Current with QuestionsGain Confidence on Magnetic Effects of Current with QuestionsGain Confidence on Magnetic Effects of Current with Questions41 mins
Test Your Knowledge of Electric Charge & Coulomb's LawTest Your Knowledge of Electric Charge & Coulomb's LawTest Your Knowledge of Electric Charge & Coulomb's Law47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :