Suppose that we have an axon that is 10 cm long, with an inner radius r1...
- Suppose that we have an axon that is 10 cm long, with an inner radius r1 of 1 μm and outer radius r2 = r1+ 1nm = 1 μm + 1nm. In this exercise, you may use a dielectric constant for cellular fluid of κ = 3.
- Write an expression for the magnitude of the Electric Field, “E” outside (at an arbitrary radius r) for a uniformly charged cylinder of length “l” with charge “q”:
- This cylinder is in a dielectric fluid, not vacuum conditions (a conducting liquid lies between the inner and outer radii of the cylinder). How does that change your expression for E with a dielectric constant κ? (This expression is in your textbook). Don’t plug in any numbers yet, just give the expression.
- Make sure you understand how the concepts of electric field and potential difference (V) are related. If you need help, ask your recitation leader. Calculate the potential difference for a cylindrical capacitor of outer radius r2 and inner radius r1 and length l. Don’t plug in any numbers yet, just give the expression. Hint: Try it on your own for practice, and if you need more help follow example 26.11 from your textbook “A cylindrical capacitor”. Note: Your expression for V will differ from the one in the book very slightly due to the dielectric medium. Make sure you use your expression from (2.) for the electric field here, which includes the given dielectric constant.
- What is the relationship between capacitance (C) and the potential difference (V) for a capacitor? Using this relationship, write down the capacitance for the axon in this activity. Give the expression, and then plug in the given values to get your answer in SI units.
If for #2, I got E = q / (2 * pi * r * l * Eo * k), how would I use this to answer #3 and #4
Homework Answers
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Suppose that we have an axon that is 10 cm long, with an
inner radius r1...
An axon is a long, slender projection of a nerve cell, or neuron e , that...
An axon is a long, slender projection of a nerve cell, or neuron e , that typically conducts electrical impulses e away from the neuron's cell body e . Capacitance (C) is the ability of a system to store an electric charge. In this activity, you'll use information given about these fascinating structures to calculate the capacitance of an axon. Αxon Axon terminal Dendrite Node of Ranvier Soma Axon Schwann cell Myelin sheath Nucleus plasma membrane cytoplasm, a conducting liquid...
The figure to the right shows a cylindrical capacitor with inner radius b and outer radius a. Between the cylinders (shaded region) is a dielectric of constant k.
The figure to the right shows a cylindrical capacitor with inner radius b and outer radius a. Between the cylinders (shaded region) is a dielectric of constant k. If the inner cylinder contains charge +Q and out charge -Q determine an expression for: The electric field in the region between the cylinders. The potential difference between in the region between the cylinders. The capacitance of the capacitor. The energy density of the capacitor
2. (4 points) A spherical capacitor has outer radius R2 and inner radius R1 and is filled with a dielectric material in which ε--Ceo/r. A positive charge Q is placed in the inner radius and a negativ...
2. (4 points) A spherical capacitor has outer radius R2 and inner radius R1 and is filled with a dielectric material in which ε--Ceo/r. A positive charge Q is placed in the inner radius and a negative charge-Q is placed on the outer radius. Remember that ε in this problem depends on the radial position r. (a) Calculate D, E and P within the capacitor, as a function of r for R R2 b) Calculate the potential V, from R1...
A spherical capacitor has a spherical inner plate with radius a and outer plate with radius...
A spherical capacitor has a spherical inner plate with radius a
and outer plate with radius b. The charge on the inner plate is +Q
and on the outer plate it is -Q. We have filled a cone shaped
region of angle θ (0 ≤ θ ≤ π) with a dielectric with constant κ.
The dielectric fills the entire volume between the two spheres
inside the cone. You may neglect any fringing effects between the
dielectric and the vacuum (dielectric...
Problem (1) A long solid metal conducting cylinder with radius a is coaxial with a long, hollow, metal conducting tube of greater radius b. The inner cylinder of radius a is positively charged with a...
Problem (1) A long solid metal conducting cylinder with radius a is coaxial with a long, hollow, metal conducting tube of greater radius b. The inner cylinder of radius a is positively charged with a positive charge per unit length of magnitude λ (C/m , and there is an equal negative charge per unit length on the outer cylinder of radius b. The region between the two cylinders is filled with an insulating material of dielectric constant K Please use...
An air-filled spherical capacitor is constructed with an inner-shell radius of 6.50 cm and an outer-shell radius of 12.6 cm
An air-filled spherical capacitor is constructed with an inner-shell radius of 6.50 cm and an outer-shell radius of 12.6 cm (a) Calculate the capacitance of the device. (b) What potential difference between the spheres results in a 4.00 μC charge on the capacitor? (c) What If? What would be the length (in cm) of a cylindrical air-filled capacitor with the same inner and outer radii as the spherical capacitor if it were to have the same capacitance as the spherical capacitor?
The long thin cylindrical axon of a nerve carries nerve impulses. The axon can be as...
The long thin cylindrical axon of a nerve carries nerve impulses. The axon can be as long as 1 m. A) Estimate the capacitance of a 1.0-m-long axon of radius 3.9 ×10−6 m with a membrane thickness of 7.6 ×10−9 m. The dielectric constant of the membrane material is about 6.0. B)Determine the magnitude of the charge on the inside (negative) and outside (positive) of the membrane wall if there is a 0.065-V potential difference across the wall. C)Determine the...
The long thin cylindrical axon of a nerve carries nerve impulses. The axon can be as...
The long thin cylindrical axon of a nerve carries nerve impulses. The axon can be as long as 1 m A) Estimate the capacitance of a 1.0-m-long axon of radius 4.2 ×10−6 m with a membrane thickness of 8.2 ×10−9 m. The dielectric constant of the membrane material is about 6.0? B) Determine the magnitude of the charge on the inside (negative) and outside (positive) of the membrane wall if there is a 0.079-V potential difference across the wall? C)...
The long thin cylindrical axon of a nerve carries nerve impulses. The axon can be as...
The long thin cylindrical axon of a nerve carries nerve impulses. The axon can be as long as 1 m. a. Estimate the capacitance of a 1.0-m-long axon of radius 3.9 ×10−6 m with a membrane thickness of 7.2 ×10−9 m. The dielectric constant of the membrane material is about 6.0. b. Determine the magnitude of the charge on the inside (negative) and outside (positive) of the membrane wall if there is a 0.077-V potential difference across the wall. c....
A long cylindrical coaxial capacitor of length ?, has an inner radius ? and an outer...
A long cylindrical coaxial capacitor of length ?, has an inner radius ? and an outer radius ?, as shown in figure (4). The capacitor is filled with one layers of an isotropic and homogenous dielectric with permittivity of 4??. If the voltage of the inner electrode is maintained at ?? while the outer electrode is earthed, calculate the following: a) Electric flux density and the electric field intensity in whole space b) The equation that describe the voltage between...
An axon is a long, slender projection of a nerve cell, or neuron e , that typically conducts electrical impulses e away from the neuron's cell body e . Capacitance (C) is the ability of a system to store an electric charge. In this activity, you'll use information given about these fascinating structures to calculate the capacitance of an axon. Αxon Axon terminal Dendrite Node of Ranvier Soma Axon Schwann cell Myelin sheath Nucleus plasma membrane cytoplasm, a conducting liquid...
2. (4 points) A spherical capacitor has outer radius R2 and inner radius R1 and is filled with a dielectric material in which ε--Ceo/r. A positive charge Q is placed in the inner radius and a negative charge-Q is placed on the outer radius. Remember that ε in this problem depends on the radial position r. (a) Calculate D, E and P within the capacitor, as a function of r for R R2 b) Calculate the potential V, from R1...
A spherical capacitor has a spherical inner plate with radius a
and outer plate with radius b. The charge on the inner plate is +Q
and on the outer plate it is -Q. We have filled a cone shaped
region of angle θ (0 ≤ θ ≤ π) with a dielectric with constant κ.
The dielectric fills the entire volume between the two spheres
inside the cone. You may neglect any fringing effects between the
dielectric and the vacuum (dielectric...
Problem (1) A long solid metal conducting cylinder with radius a is coaxial with a long, hollow, metal conducting tube of greater radius b. The inner cylinder of radius a is positively charged with a positive charge per unit length of magnitude λ (C/m , and there is an equal negative charge per unit length on the outer cylinder of radius b. The region between the two cylinders is filled with an insulating material of dielectric constant K Please use...
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