A thin half ring of radius 35 cm is uniformly charged with a total charge Q.

The electric field at the centre of the half ring is 100 V/m.

Find the value of Q in nano-coulomb (nC).

Options:

• (1) 2.14
• (2) 0.7
• (3) 2.44
• (4) 3.25

For a uniformly charged semicircular ring, the electric field at the centre is:

E = 2kQ / πR²

Given:

• E = 100 N/C
• R = 35 cm = 0.35 m
• k = 9 × 10⁹ N m²/C²

Substituting:

100 = 2 × 9 × 10⁹ × Q / (3.14 × 0.35²)

Solving:

Q ≈ 2.14 × 10⁻⁹ C

Therefore:

Q = 2.14 nC

Final Answer

Option (1) 2.14 nC