Question

1.A neuron is a cell which carries electric current. Suppose that a neuron has a 6.0 nm thick membrane. Its outside and inside surfaces contain charge, and the dielectric constant of the membrane is 7.0. Estimate, to one significant figure, the capacitance of this membrane per m2 by modeling it as a parallel-plate capacitor.

2. Charges −q and q are placed at the points (0, d/2) and (0, −d/2), respectively. A third charge +Q is placed at (s, 0). Find the total electric force on +Q.

3.Two equal and positive point charges are stuck to the points (−1, 0) and (1, 0). What is the magnitude of the potential difference between points (0, 1) and (0, 2)?

4.In a one-dimensional space, there is an electric potential V = −2x + 5, in V . What force does a charge q > 0 feel upon being placed at (10, 0)?

Answer 1

(1) We know that capacitance
C = kA/d
where K is dielectric constant
C/A = k/d
C/A = 7*8.85*10^-12 /(6*10^-9) = 10.325*10^-3 m
(2)  
Force between the two charges
F₁ = F₂ = KqQ / r²
where r = [(d/2)² +s²]^1/2
F₁ = F₂ = KqQ / [(d/2)² +s²]
Now
On taking the component of forces along the horizontal and vertical
we notice that horizontal component will cancel each other.
Therefore
the net force will be
= F₁Sin + F₂Sin
= 2F₁Sin
= 2*(KqQ / [(d/2)² +s²])*(d/2s)
Hence this will be the net force on the Q charge.
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