Practice portal › Electric Charge and Properties › Field of Spheres, Shells and Cylinders

The electric field produced by an infinitely long, straight, uniformly charged wire at a perpendicular distance of 2 cm is 3×10⁸ N C⁻¹. The linear charge density on the wire is ________. (K=9×10⁹ SI unit)

Asked in GUJCET 2014 · Charged cylinder and line charge

• (1) 333 μC m⁻¹
• (2) 3.33 μC m⁻¹
• (3) 666 μC m⁻¹
• (4) 6.66 μC m⁻¹

Step-by-step solution

Why the other options are wrong

• (2) Right digits, wrong power of ten: λ=3.33×10⁻⁴ C m⁻¹, and 10⁻⁴ C is 100 μC, so this is 333 μC m⁻¹, not 3.33.
• (3) Drops the 2 in E=(2Kλ)/r: using E=(Kλ)/r gives λ=(Er)/K=666 μC m⁻¹, twice too large.
• (4) Uses r² in place of r, as for a point charge: λ=(Er²)/(2K)≈6.66 μC m⁻¹. A line charge's field falls as 1/r, not 1/(r²).

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.