BIO STIMULATING THE BRAIN. Communication in the nervous system is based on the propagation of electrical signals called action potentials along axons, which are extensions of nerve cells (see the Passage Problems in Chapter 26). Action potentials are generated when the electric potential difference across the membrane of the nerve cell changes: Specifically, the inside of the cell becomes more positive. Researchers in clinical medicine and neurobiology cannot stimulate nerves (even noninvasively) at specific locations in conscious human subjects. Using electrodes to apply current to the skin is painful and requires large currents, which could be dangerous.
Anthony Barker and colleagues at the University of Sheffield in England developed a technique called transcranial magnetic stimulation (TMS). In this widely used procedure, a coil positioned near the skull produces a time-varying magnetic field that induces in the
29.72 Consider the brain tissue at the level of the dashed line to be a series of concentric circles, each behaving independently of the others. Where will the induced emf be the greatest? (a) At the center of the dashed line; (b) at the periphery of the dashed line; (c) nowhere—it will be the same in all concentric circles; (d) at the center while the stimulating current increases, at the periphery while the current decreases.
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- Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed pulse duration = 50.0 m/s 2.0 103 s = 0.10 m). In the resting state, the outer surface of the axon wall is charged positively with K+ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in Figure P18.43. Model the axon as a parallel-plate capacitor and take C = 0A/d and Q = C V to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.0 108 m, axon radius r = 1.0 101 m, and cell-wall dielectric constant = 3.0. (a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 102 V? Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge e per squared (2). An atom has a cross section of about 1 2 (1 = 1010 m). (b) How much positive charge must flow through the cell membrane to reach the excited state of + 3.0 102 V from the resting state of 7.0 102 V? How many sodium ions (Na+) is this? (c) If it takes 2.0 ms for the Na+ ions to enter the axon, what is the average current in the axon wall in this process? (d) How much energy does it take to raise the potential of the inner axon wall to + 3.0 102 V, starting from the resting potential of 7.0 102 V? Figure P18.43 Problem 43 and 44.arrow_forwardNerve cells in your body can be electrically stimulated; a large enough change in a membrane potential triggers a nerve impulse. Certain plants work the same way. A touch to mimosa pudica, the “sensitive plant,” causes the leaflets to fold inward and droop. We can trigger this response electrically as well. In one experiment, investigators placed electrodes on the thick tissue at the base of a leaf. The electrodes were 3.5 mm apart. When the electrodes were connected to a 47 μF capacitor charged to 1.5 V, this stimulated a response from the plant.a. Eventually, all the charge on the capacitor was transferred to the plant. How much charge was transferred?b. What was the approximate electric field between the electrodes?arrow_forwardMeasuring Blood Flow. Blood contains positive and negative ions and thus is a conductor. A blood vessel, therefore, can be viewed as an electrical wire. We can even picture the flowing blood as a series of parallel conducting slabs whose thickness is the diameter 5.00 mm of the vessel moving with speed. (See in the following figure.(Figure 1)) Figure X X BX X X X X X X X X d 1 of 1 V potential difference of 1.00 mV ? Express your answer with the appropriate units. B = 1.31 T Submit Part C Correct R= Determine the volume rate of flow (R). (Note: Although the method developed here is useful in measuring the rate of blood flow in a vessel, it is limited to use in surgery because measurement of the potential & must be made directly across the vessel.) Express your answer in terms of some or all of the variables B, d, v, and E. Previous Answers A cylindrical blood vessel in a magnetic field. av 4B Submit ΑΣΦ Provide Feedback Bw Previous Answers Request Answer ? X Incorrect; Try Again; 3…arrow_forward
- Measuring Blood Flow. Blood contains positive and negative ions and thus is a conductor. A blood vessel, therefore, can be viewed as an electrical wire. We can even picture the flowing blood as a series of parallel conducting slabs whose thickness is the diameter 5.00 mm of the vessel moving with speed. (See in the following figure.( Figure 1)) Figure X XBX X XX X X X X d 1 of 1 V If you expect that the blood will be flowing at 15.3 cm/s for a vessel 5.00 mm in diameter, what strength of magnetic field will you need to produce a potential difference of 1.00 mV ? Express your answer with the appropriate units. B = Submit Part C 0 R = μA Submit Value X Incorrect; Try Again; 5 attempts remaining T Previous Answers Request Answer = VE ΑΣΦ Determine the volume rate of flow (R). (Note: Although the method developed here is useful in measuring the rate of blood flow in a vessel, it is limited to use in surgery because measurement of the potential & must be made directly across the vessel.)…arrow_forwardIn Example 23.14 we estimated the capacitance of the cell membrane to be 89 pF, and in Example 23.15 we found that approximately 10,000 Na+ ions flow through an ion channel when it opens. Based on this information and what you learned about the action potential, estimate the total number of sodium channels in the membrane of a nerve cell.arrow_forwardApplying Kirchhoff's Laws to the electrical network in the figure, the currents I1, I2, and I3 are the solution of the system I1 211 + 312 I2 + I3 = 0 = 16 312 + 513 : 22 where a = 2, b = 3, c = 5, v1 16, and v2 = 22. Find the currents. I2 = Iз a Q' V, volts V2 volts IIarrow_forward
- Every cell in the body has organelles called mitochondria that can generate a voltage difference between their interior and exterior. If the capacitance of a mitochondrion is 4.0×10−11F and the potential difference between the interior and exterior is 0.18 V, how much electrical energy does it store? If a mitochondrion were to use all of its stored electrical energy to produce ATP molecules, and each ATP molecule requires 9.5×10−20J, how many molecules could it produce? (In reality, ATP molecules are produced by the flow of protons caused by the proton motive force, and not by the direct conversion of electrical energy stored by the capacitance of mitochondria.)arrow_forwardNeurons are components of the nervous system of the body that transmit signals as electric impulses travel along their length. These impulses propagate when charge suddenly rushes into and then out of a part of the neuron called an axon. Measurements have shown that, during the inflow part of this cycle, approximately 5.6 x 1011 Na+ (sodium ions) per meter, each with charge +e, enter the axon. How many coulombs of charge enter a 1.5-cm length of the axon during this process?arrow_forwardA myelinated axon conducts nerve impulses at a speed of 40 m/s. What is the signal speed if the thickness of the myelin sheath is halved but no other changes are made to the axon?arrow_forward
- A circuit has a 42.3 pF capacitor, a 59.6 pF capacitor and a 69.4 pF capacitor in parallel with each other. What is the equivalent capacitance (in pico-Farads) of these three capacitors?arrow_forwardA/An is a unit equal to one joule per coulomb. volt O capacitor сараcitance electric field linearrow_forwardIn the circuit below R1 = 10 ohms, R2 = 20 ohms, R3 C2 = 10 microF, C3 = 10 microF and V= 100 volts. a) What is the time constant 10 ohms, C1 = 10 microF, %3D %3D %3D of the circuit? (microseconds) R1 R2 -R3 V C1 C2 C3arrow_forward
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