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For a capacitor the distance between the two plates is 5x and the electric field between them is E₀. Now a dielectric slab having dielectric constant 3 and thickness x is placed between them in contact with one plate. In this condition, what is the potential difference between the two plates?

Asked in GSEB Board July 2016 · Dielectric slab

• (1) 15E₀x
• (2) (13E₀x)/3
• (3) 7E₀x
• (4) (9E₀x)/2

Step-by-step solution

Why the other options are wrong

• (1) Comes from multiplying the original potential difference 5E₀x by K=3. A dielectric weakens the field inside it rather than multiplying the voltage, and here it fills only a fifth of the gap.
• (3) Multiplies the field inside the slab by K instead of dividing: 4E₀x+3E₀x=7E₀x. Bound charges on the slab's faces oppose the field, so inside it the field is (E₀)/3.
• (4) No single slip produces (9E₀x)/2. Sanity check: the air gap of 4x carries 4E₀x and the slab carries (E₀)/3× x, so the total is (13E₀x)/3≈4.33E₀x, not 4.5E₀x.

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