JEE/NEET Physics · Electrostatics series · Part 5 of 8 · All parts →
- In a conductor, charges are free to move — and they move until the interior field is zero
- Any net charge on a conductor sits entirely on its OUTER surface
- The cavity inside a conductor is field-free: the Faraday cage
- Field lines meet conductors perpendicular; sharp points concentrate field
- Shielding works one way: outside fields are blocked, inside charges still matter
Step into a lift and your phone drops a bar. Sit inside a metal plane and lightning hits it — you’re fine. Both are the same physics: conductors rearrange their own charges to make their interiors field-free. Part 5 of the Electrostatics series.
- What a conductor really is
- The rearrangement argument
- Charge lives on the surface
- The Faraday cage
- Sharp points and corona
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
What a Conductor Really Is
In metals, the outer electrons belong to the whole crystal — a mobile sea, free to drift. So place a conductor in any electric field and the sea responds instantly: electrons drift against the field, piling up on one side, leaving the other side positive. These piled charges create their own field.
The Rearrangement Argument
The drift stops only when the internal field is cancelled exactly:
Three consequences follow like dominoes: (1) since E = 0 inside, the potential is CONSTANT throughout a conductor (flat landscape, Part 3); (2) any excess charge you add must sit on the OUTER surface (Gauss: zero internal field → zero enclosed charge); (3) field lines meet the surface perpendicular — any parallel component would drag surface charges along.
Charge Lives on the Surface
Add charge to a metal sphere: it spreads over the outer skin, never the interior. On curved surfaces, the charge crowds where curvature is greatest — a sphere spreads evenly, but a pointed tip collects charge densely, making the local field enormous.
The Faraday Cage
Put a cavity inside a conductor — a metal box, a car body, a plane fuselage. Whatever external fields rage outside, the rearranged surface charges cancel them within the metal, and the cavity stays field-free. That’s the Faraday cage — shielding electronics, protecting you in a lightning-struck car (it’s the metal cage, not the rubber tyres!).
Sharp Points and Corona
Dense charge at a sharp tip → extreme local field → air itself ionises → a faint violet glow (corona) and charge leaks away. Lightning rods invite the strike by making the first tiny breakdown happen at their tips. For the same reason, high-voltage equipment avoids sharp edges — rounded terminals, toroidal rings.
Solved Examples
All Q on the outer surface. E = 0 in the metal (conductor rule) and in the cavity (no enclosed charge, Gauss).
Outside: the sphere acts as a point charge Q at centre — kQ/r². The three-zone picture (cavity zero, metal zero, outside point-like) is the exam standard. ✔
Answer: Q on outer surface; E = 0 inside everywhere; kQ/r² outside
Connected = one conductor = one potential: kq₁/R = kq₂/r → q ∝ radius.
Bigger sphere keeps proportionally more charge (Q·R/(R+r) on the big one) — but the smaller sphere ends up with DENSER surface charge and a STRONGER surface field. That’s why points and small radii spark first. ✔
Answer: q ∝ radius; small sphere has stronger surface field
Outside charge: the shell’s surfaces rearrange, interior cavity field = 0 — shielded.
Inside charge (+q in the cavity): −q appears on the cavity wall, +q on the outer surface — the exterior field is that of +q at centre. Shielding blocks outside-in, NOT inside-out. This asymmetry is a JEE favourite. ✔
Answer: outside-in blocked; inside-out not — outer field = +q’s
- ‘E = 0 inside’ used for insulators. Only free charges rearrange — insulators keep fields inside. The conductor rule is about mobile charge.
- Charge inside a cavity counting as ‘inside the conductor’. A charge in the cavity is NOT in the metal — it induces −q on the cavity wall and +q outside. Gauss through the metal still sees zero.
- Believing the car-in-lightning safety is the tyres. It’s the metal cage conducting the strike around the occupants. Motorcyclists get no such cage — hence the difference.
- Uniform charge on irregular shapes. Charge density follows curvature: sharp = dense. Spheres only spread evenly.
This Physics in Your Daily Life
- Car struck by lightning, occupants unharmed: the body is a Faraday cage — the strike travels in the metal, around you.
- Phone dead in a lift: the shaft’s steel cabin is an accidental Faraday cage blocking the signal — physics you enter daily.
- MRI rooms and labs are shielded with copper mesh so external radio noise can’t blur the image — engineered cages, metres large.
- Lightning rods exploit the sharp-point field concentration to take the strike safely — corona engineering, 1752 to today.
- Wrapped-in-foil test: wrap a phone in aluminium foil and call it — straight to voicemail. Faraday’s demo, kitchen-sized.
Practice set (answers hidden — try first)
(NEET-level) E inside a charged conductor at equilibrium:
(NEET-level) Excess charge given to a conductor resides:
(Concept) A person inside a car struck by lightning is safe because:
(JEE Main-level) A charge inside a conductor’s cavity induces:
(Concept) Field lines at a conductor’s surface:
- E = 0 inside conductors (static)
- charge → outer surface; cavity shielded
- 🔣 free charges rearrange until E inside a conductor = 0
- 🔣 net charge sits on the outer surface; cavity is field-free
- 🔣 Faraday cage: blocks outside fields (not inside charges)
- 🔣 field lines hit conductor surfaces perpendicular
- 🔣 sharp points concentrate field → corona → lightning rods
- 🔁 E = 0 inside a conductor at equilibrium
- 🔁 excess charge on the outer surface
- 🔁 cavity = field-free (Faraday cage)
- 🧠 Chant: ‘charges move until the inside goes quiet’.
- 🧠 Shield asymmetry: ‘the cage blocks coming-in, not going-out’.
- 🏠 Daily: lift-signal loss and lightning-safe cars — Faraday cages you ride in.
- 🏠 Daily: the foil-wrapped phone test — a kitchen Faraday demo.
Quick revision
- In a conductor, charges are free to move — and they move until the interior field is zero
- Any net charge on a conductor sits entirely on its OUTER surface
- The cavity inside a conductor is field-free: the Faraday cage
- Field lines meet conductors perpendicular; sharp points concentrate field
- Shielding works one way: outside fields are blocked, inside charges still matter
- What a conductor really is
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