1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# If O is the center of a ring of radius r, then find the potential at point O due to half ring that has a linear charge density λ.

A
λ4ϵ0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
λ4π2ϵ0r
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
λ4πϵ0r
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
λ4πϵ0r2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A λ4ϵ0Let us consider a small element on ring of length dl as shown in figure. Charge on the element, dq=λdl=λ(rdθ) Potential due to a charge element dq at a distance r is dV=14πϵ0dqr Substituting the value of dq we get, dV=14πϵ0λrdθr ⇒dV=λdθ4πϵ0 Now potential at the centre due to half ring will be, V=π2∫−π2λdθ4πϵ0 ⇒V=λ4πϵ0 θ ∣∣∣π2−π2 ⇒V=λπ4πϵ0 ∴V=λ4ϵ0 Hence, option (a) is the correct answer.

Suggest Corrections
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program