The voltage sensitivities of Barium Titanate and Quartz are respectively 12 × 10-3 Vm / N and 50 × 10-3 Vm / N. their respective permittivities are 12.5 × 10-9 F / m and 40.6 × 10-12 F / m. What are their charge sensitivities?

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  1. 1.04 × 106 C / N and 1.23 × 109 C / N
  2. 150 pC / N and 2 pC / N
  3. 24.5 pC / N and 90.6 pC / N
  4. 0.9 × 106 C / N and 1.23 × 109 C / N

Answer (Detailed Solution Below)

Option 2 : 150 pC / N and 2 pC / N
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Detailed Solution

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The charge sensitivity of a material is defined as the multiplication of voltage sensitivity and its permittivity.

Charge sensitivity = Voltage sensitivity × permittivity

Voltage sensitivity of Barium titanate, Vsen1 = 12 × 10-3 Vm / N

Voltage sensitivity of Quartz, Vsen2 = 50 × 10-3 Vm / N

Permittivity of Barium titanate, ε1 = 12.5 × 10-9 F / m

Permittivity of Quartz, ε2 = 40.6 × 10-12 F / m

Charge sensitivity = Voltage sensitivity × permittivity

For barium Titanate,

Charge sensitivity = Vsen1 × ε1

= 12 × 10-3 × 12.5 × 10-9

= 150 × 10-12 C / N

= 150 pC / N

For Quartz, charge sensitivity = Vsen2 × ε2

= 50 × 10-3 × 40.6 × 10-12

= 2030 × 10-15 C / N

= 2.03 pC / N

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