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Answer :
Final answer:
To calculate the electric field just above the center of the nonconducting disk, use the formula E = σ/2ε₀, where E is the electric field, σ is the charge density, and ε₀ is the permittivity of free space.
Explanation:
To calculate the electric field just above the center of the nonconducting disk, we can use the formula for electric field due to a uniformly charged disk:
E = σ/2ε₀, where E is the electric field, σ is the charge density, and ε₀ is the permittivity of free space.
Since the charge is spread uniformly over the surface of the disk, the charge density σ = Q/A, where Q is the charge and A is the area.
Given Q = -5.00 nC and A = πr² (the area of a disk), with r = 1.00 cm, we can calculate σ.
Plugging in the values, we get σ = (-5.00 nC) / (π*(0.01 m)²).
Next, plugging the value of σ into the equation for electric field, we get E = σ/2ε₀.
Finally, we can calculate the magnitude and direction of the electric field by evaluating the expression.
Thus: σ = Q / A = -5.00 × 10⁻⁹ C/π(0.01m)² = -1.59 × 10⁻⁴ C/m².
Substituting σ and ε₀ values into the formula: E = σ / (2ε₀) = -1.59 × 10⁻⁴ C/m² / (2) × (8.85 × 10⁻¹² C²/N·m²) = -8.97 × 10 Tens C/m². Considering a precision of two digits from question, E is approximately -9.00 N/C. So, none of the options listed (a) 5.00 N/C, b) 10.0 N/C, c) -5.00 N/C and d) -10.0 N/C) is correct. The answer should be close to -9.00 N/C.
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