Question : The linear charge density on the circumference of a circle of radius 'a' varies as λ=λ₀cosθ. The total charge on it is
a) Zero
b) Infinite
c) πaλ₀
d) 2πa
Doubt by Yashika
Solution :
We know,
dq=λdl
dq=λdl
Also
Angle (θ) = length of arc (l) / radius (r)
θ = l/a
l =aθ
dl =adθ
Angle (θ) = length of arc (l) / radius (r)
θ = l/a
l =aθ
dl =adθ
so,
dq=λadθ
dq=[λ₀cosθ]adθ [⸪λ=λ₀cosθ]
dq=aλ₀cosθdθ
dq=λadθ
dq=[λ₀cosθ]adθ [⸪λ=λ₀cosθ]
dq=aλ₀cosθdθ
In order to obtain total charge, we need to integrate the above expression within proper limits.
