Two point charges are on the y-axis. A 5.0 C charge is located at y cm, and a-2.

Question

Two point charges are on the y-axis. A 5.0 C charge is located at y cm, and a-2.06 pC charge is located at y =-1.00 cm. 1.00 (a) Find the total electric potential at the origin. (b) Find the total electric potential at the point having coordinates (1.50 cm, 0) Need Help? Show My Work (optional) Question Details Ask Your A parallel-plate capacitor with area 0.100 m2 and plate separation of 1.00 mm is connected to a 21.00 V battery. (a) What is the capacitance? (b) How much charge is stored on the plates? (c) What is the electric field between the plates? N/C (d) Find the magnitude of the charge density on each plate. C/m2 (e) Without disconnecting the battery, the plates are moved farther apart. Qualitatively, what happens to each of the previous answers?

Explanation / Answer

Part A
Charge, q1 = 5.0*10^-6 C

Charge, q2 = - 2.06 *10^-6 C

(a) Distance of charge q1, r1 = 1.0 cm
= 0.01 m
Distance of charge q2, r2 = 1.0 cm
= 0.01 m

Total electric potential

V = k [ (q1 / r1 ) + ( q2 / r2 ) ]
  
= 9 *10^9 * 10^-6 * [ (5 / 0.01) + (-2.06 / 0.01 ) ]

= 9 *10^3 * ( 500 - 206)

= 2.646*10^6 V

(b) Distance of charge q1, r1 = sqrt(1.5^2 + 1.0^2)
= 1.80 cm
= 0.018 m   
Distance of charge q2, r2 = sqrt(1.5^2 + 1.0^2)
= 1.80 cm
= 0.018 m

Total electric potential

V = k [ (q1 / r1 ) + ( q2 / r2 ) ]

= 9 *10^9 * 10^-6 * [ (5.0/ 0.018) + (-2.06 / 0.018) ]

= 9 *10^3 * ( 277.78 - 114.45 )

= 1.469*10^6 V

Part B

(a) Capacitance, C
  
= Eo * (A/d)
= 8.9 *10^-12 * (0.100/0.001) * 10^6 uF
= 8.9*10^-4 uF.

(b) Charge stored, Q
  
= C*V
= 8.9*10^-4 * 21 C
= 186.9*10^-4 C

(c) Electric field, E

= V/d
= 21/(0.001) V/m (or N/C)
= 21000 V/m (or N/C)

(d) Magnitude of charge density on each plate

= Q/A
= 186.9*10^-4 / (0.100)
= 0.1869 C/m^2

(e) d increases

C = E0 * (A/d) decreases as A is constant
Q = CV also decreases as C decreases with V remaining the same
E = V/d decreases as V is constant
Ac = C decreases and A is constant, magnitude of charge density on each plate,
C/A decreases.

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