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Problem 44 Hard Difficulty

Consider the model of the axon as a capacitor from Problem 43 and Figure P 18.43. (a) How much energy does it take to restore the inner wall of the axon to $-7.0 \times 10^{-2} \mathrm{V}$ , starting from $+3.0 \times 10^{-2} \mathrm{V}$ ? (b) Find the average current in the axon wall during this process.

Answer

a.$F_{A}=4 \cdot 08 \times 10^{-11} \mathrm{~J}$
b.$5.56 \times 10^{-7} A$

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Video Transcript

in this particular problem, we need to first calculated the energy in order to restore the inner wall off takes on We first need to joint down the day you die here to start from step. Eh? Here the lent off the eggs on membrane is equal to El is equal to 10 centimetres was converted into a major first. So do you worry about 100? So 0.1 mega next day that would be radius. So radius off gigs on is equal to small are giving us then micrometer o r. It's one include Ennis to minus five meter. We can unique reggae jazz turned into Venice to minus six meters. They told about every able to be Katya off the service off exam membrane, and that would be denoted as e. It is length times Jubair. So now to calculate that therefore is equal to lengthy 0.1 meter and you do bye into 10 include generous to minus six meter, which is a value far so finally area of the surface. Off the exam memory is equal to 6.283 include Ennis to minus six, made a square. Let's put the bracket good next. Oh, let's talk about the Celtic nous. So right here in Syria thickness which is denoted as D, which is one in organist to minus age meters. Oh, now it will be die electric constant. So die electric constant off the wall is equal to K is equal to 3.0 or you can even mention it. A street is the typical value of the dialectic constant No will go a step further. Well calculated. The value of the capacity is therefore capacitance is equal to see which is que multiplied by absolute zero multiplied by a DEA Do I did about thickness. So now absolute zero is basically bomb acuity of the free space who has difficult value So therefore seize equality tree multiplied by 8.85 into tennis to minus trail C square with respect oh u turn Mito square. This is a typical value of form activity off the face piece multiplied by area, which were already calculated to point six point to a tree into tennis to minus six minusca and let us do our does by Celtic nous. So that is one include tennis to minus eight media finally well calculating this, we get the value of C as 1.6 succeed in glutinous to minus eight Freds. Since it's a capacitance, the DIS mocked us no further. Consider the given mortgage. In this case, given mortgage is equal to minus 17 too generous to minus tools. Now we already know that Q is equal to product off capacities toward it. That is totally charges in court. Do capacitance and old age. My application. So therefore, it will be 1.668 Include generous to minus eat friends multiplied by seven into tennis to minus two worlds. We may not consider the minus sign here. When calculating the door ajar, Sochi was equal to 1.167 Include generous to minus nine columns. This is the amount off charge gathered now, so let energy it takes restore the potential off in exam be denoted as e. So, Catherine, you know, which is the final answer for Step A Jozic will do. It will be in terms of kinetic energy so half into sea in Dewey Square. So let us put the values here see as 1.668 into tennis to minus it. Indu while you're free. Seven include generous to minus two the whole square. So finally we get down sir s 4.8 indu tennis to minus 11 jewels because since its energy So everything comes off Julie's and this is the final answer for Step A which is the energy required to restore the potential off inner eggs on water. Let's Morehead instead be we need to find average current Indo his own morning. Okay, now here first will continue to re charge on the inner membrane. So let Children charge on inner membrane be que dish So therefore cued ashes they will do see time's read ash will even change the no additional word ish since it's a another war dish. So well, you see, we already got 1.66 feet in pretenders to minus eight friends multiplied by three, including Agnes to minus two world which is given value Day four finally ready of Q Dash is five into tennis to minus 10 blooms. Let's mark this thus we can nation it was in your charge. Six monkey is equal to Q dash minus off my rescue since we need to get the value off net prosecutors. We do the subtraction. So therefore Q is equal to now. Let us mation if I in group and is to minus 10 minus minus off 1.167 in group in this two minus night. We need to do this calculation carefully. Day four It is 1.667 into tennis, too minus nine colognes. So this is the next positive charge venue that we have guard. No, we need to calculate the average current. So current is major in terms of charged with respect to time summation here, considering considering dying to return. Do the initial stayed. He's equal to three milliseconds. That means 0.3 seconds. So that's covered the current, which is denoted as I and regeneration off Q and T is equal to 1.667 into tennis to minus nine columns upon three milliseconds. City, 0.3 seconds to the value which we get here is Fi going 56 into tennis to minus seven Amperes. Very smart. This is answer, and this is the value of average current in the exam board

Top Physics 102 Electricity and Magnetism Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

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Farnaz M.

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University of Winnipeg

Physics 102 Electricity and Magnetism Bootcamp

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