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

Two infinitely long thin straight parallel wires are kept a perpendicular distance of 2R having uniform linear charge densities +λ and -λ respectively. The magnitude of electric field at a mid point between two wires will be ________.

Asked in GUJCET 2026 · Charged cylinder and line charge

• (1) λ/(πε₀R)
• (2) (2λ)/(πε₀R)
• (3) λ/(2πε₀R)
• (4) λ/(4πε₀R)

Step-by-step solution

Why the other options are wrong

• (2) Twice the correct field. It comes from taking each wire to be R/2 from the midpoint, as if the separation were R: each field becomes λ/(πε₀R) and the sum doubles again. The wires are 2R apart, so each is R away.
• (3) This is the field of one wire alone. The second wire contributes just as much at the midpoint, and in the same direction, so the two add.
• (4) One wire's field evaluated at the full separation 2R instead of at R, with the second wire left out as well - two slips at once, and no single slip gives it. Sanity check: with each wire R away and both fields adding, E=λ/(πε₀R), four times this.

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