A solid cylinder of radius R and length L carries a uniform charge density + ρ between r = 0 and r = R s and an equal charge density of opposite sign – ρ , between r = R s and r = R. What must be the radius R s so that on rotation of the cylinder about its axis the magnetic moment is zero?
Text Solution
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Sol . The magnetic moment of positively charged section of cylinder
μ + = 
× 
× π r 2 = ρπω L 
= 
ρπω LR
4 Magnetic moment of negatively charged section
µ - = – 
π r
2
= – ρπω L 
= – 
ρπω LR (R 4 – 
)
Both the magnetic moments point in the opposite direction.
= 
+ 
| 
| = μ 1 – μ 2 = 0
µ 1 = μ 2
= – 
πρω L(R 4 – 
)
R 4 = – R 4 + 
R s = 2 –1/4 R
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