Processing math: 100%
All
BE/B.Tech
MBA/PGDM
MBBS
ME/M.Tech
B.Sc
BA
B.Com
BCA
BBA/BMS
B.Sc (Nursing)

Ranking

College ranked based on real data

Indiatoday - 1740
Collegedunia - 1406
IIRF - 1684
Outlook - 1318
NIRF - 1301
Top Ranked Colleges in India ›

Find Colleges

Discover 19000+ colleges via preferences

Best MBA colleges in India
Best BTech colleges in India
Discover Top Colleges in India ›

Compare Colleges

Compare on the basis of rank, fees, etc.

IIT Madras vs IIT Delhi
IIT Madras vs IIT Bombay
Compare Colleges ›

Exams

Know more about your exams

B.Com
B.Sc
B.Sc (Nursing)
BA
BBA/BMS
BCA
BE/B.Tech
Check All Entrance Exams in India ›

College Predictor

Know your college admission chances

JEE Main
JEE Advanced
CAT
NEET
GATE
NMAT
MAT
XAT
Find Where you may get Admission ›

Course Finder

Discover top courses in Indian Colleges 2025

BE/B.Tech - 963
MBA/PGDM - 1159
ME/M.Tech - 1221
B.Sc - 1052
Get Top Courses in Indian Colleges ›

Your Gateway to Top Colleges & Exams

Discover thousands of questions, past papers, college details and all exam insights – in one place.

Popular Colleges

Top Exams

JEE MainJEE Main
JEE AdvJEE Advanced
NEET UGNEET UG
BITSATBITSAT
COMEDKCOMEDK
VITEEEVITEEE
WBJEEWBJEE

Paragraph: A point charge Q is moving in a circular orbit of radius...

Paragraph:

A point charge Q is moving in a circular orbit of radius R in the x−y plane with an angular velocity ω. This can be considered as equivalent to a loop carrying a steady current Qω2π. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant γ.


Question:

The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is
-γ BQR2
-γ BQR22
γ BQR22
γ BQR2
Solution:
Magnetic dipole moment M=γJ
ΔM=γΔJ ...(1)
ΔJΔt=-QdBdt·R2R
ΔJ=-QB2R2
So ΔM=-γQBR22
Alternate

ML=Q2m
M=Qω2ππR2=QωR22
induced electric field is opposite to the ω so the charge is retarded.
ω′=ω-αt
ω′=ω-QB21(at=QE/m),(α=QEmR=QR×BR2m=QB2m)
Mf=Qω′R22=Q(ω-QB2m)R22
∆M=Mf-Mi=QωR22-Q2BR24m-QωR22=-γBQR22