Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment m. Which configuration has highest net magnetic dipole moment ? [figure]
- (1)
- (2)
- (3)
- (4)
Answer
(3) (3)
Solution
Magnetic dipole moment points from S to N of each magnet. For two equal moments m inclined at angle θ:
mnet = m2 + m2 + 2m2 = 2m 2
(1) = 90 ⇒ mnet = 2 m = 1.41 m
(2) = 180 ⇒ mnet = 0
(3) = 30 ⇒ mnet = 2m 15 = 1.93 m
(4) = 60 ⇒ mnet = 2m 30 = 1.73 m
Configuration (3) has the highest net magnetic dipole moment.
Answer: (3)