15 marks Many fish and other aquatic animals can detect electric fields. A famous example is...
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15 marks Many fish and other aquatic animals can detect electric fields. A famous example is sharks whose sensitivity to electric fields is sufficient to detect the EMF induced in their body as they move through the Earth's magnetic field. The electrically sensitive part of the shark is known as the ampullary organ. We can think of the ampullary organ as a highly conductive rod of length 1 surrounded by highly resistive parts of the body of the shark. An electric field in the ampullary organ causes a current to flow along the rod, out through the resistive body, and back to the start of the rod through the conductive ocean water. We will use R to represent the total resistance of this circuit. At the end of the ampullary organ is a receptor that actually generates the electric signal that travels to the shark's brain. We can think of the receptor as a resistor of resistance R, which develops a voltage across it due to the current flowing. This voltage ultimately triggers neurons to carry a message to the brain. (The total resistance R includes the contribution of the receptor.) The ampullary organ of a shark can detect electric fields between 5 nV/cm and about 1 μV/cm. We will suppose that the electric field in the ampullary organ is generated by the EMF induced as a conductor is moved through the Earth's magnetic field. (a) Suppose that the shark has an ampullary organ oriented vertically. Find an expression for the potential difference between each end of the rod for a shark moving with velocity v in a magnetic field B. (b) Draw an effective circuit diagram for the ampullary organ, showing the EMF due to the shark's motion, a resistor for the receptor, and a resistor representing the rest of the shark's body. (c) Find an expression for the voltage across the receptor. (d) For a shark swimming in Sydney harbour at 0.5 m/s what is the size of this EMF per centimetre of rod in the ampullary organ. (e) Is this electric field in the range that can be detected by a shark? (f) Suppose that Rr/R~ 0.5 and rod is 10 cm long, what must be the minimum and maximum detectable voltages across the receptor? How does this compare to the typical voltage across a cell wall? (g) As the shark moves it swings its head left and right relative to its body at angular frequency w. The angle between the shark's head and its body is 0= a sin(wt). The body of the shark continues to move with constant velocity & the constant velocity of the shark's body. If a is small, find an expression for the EMF as a function of time. (h) The horizontal component of the magnetic field B points north. Find approximate expressions for the time dependence of the signal seen by the shark when it is moving in a horizontal direction: north, south, cast, and west. (i) Comment on which directions result in the largest time dependence of the EMF. Is it possible to tell north from south or cast from west? Think about the fact that the shark knows both which direction its head is moving and the sign of V. (j) Why do you think that many aquatic vertebrates can sense electric fields, but very few terrestial vertebrates can? 15 marks Many fish and other aquatic animals can detect electric fields. A famous example is sharks whose sensitivity to electric fields is sufficient to detect the EMF induced in their body as they move through the Earth's magnetic field. The electrically sensitive part of the shark is known as the ampullary organ. We can think of the ampullary organ as a highly conductive rod of length 1 surrounded by highly resistive parts of the body of the shark. An electric field in the ampullary organ causes a current to flow along the rod, out through the resistive body, and back to the start of the rod through the conductive ocean water. We will use R to represent the total resistance of this circuit. At the end of the ampullary organ is a receptor that actually generates the electric signal that travels to the shark's brain. We can think of the receptor as a resistor of resistance R, which develops a voltage across it due to the current flowing. This voltage ultimately triggers neurons to carry a message to the brain. (The total resistance R includes the contribution of the receptor.) The ampullary organ of a shark can detect electric fields between 5 nV/cm and about 1 μV/cm. We will suppose that the electric field in the ampullary organ is generated by the EMF induced as a conductor is moved through the Earth's magnetic field. (a) Suppose that the shark has an ampullary organ oriented vertically. Find an expression for the potential difference between each end of the rod for a shark moving with velocity v in a magnetic field B. (b) Draw an effective circuit diagram for the ampullary organ, showing the EMF due to the shark's motion, a resistor for the receptor, and a resistor representing the rest of the shark's body. (c) Find an expression for the voltage across the receptor. (d) For a shark swimming in Sydney harbour at 0.5 m/s what is the size of this EMF per centimetre of rod in the ampullary organ. (e) Is this electric field in the range that can be detected by a shark? (f) Suppose that Rr/R~ 0.5 and rod is 10 cm long, what must be the minimum and maximum detectable voltages across the receptor? How does this compare to the typical voltage across a cell wall? (g) As the shark moves it swings its head left and right relative to its body at angular frequency w. The angle between the shark's head and its body is 0= a sin(wt). The body of the shark continues to move with constant velocity & the constant velocity of the shark's body. If a is small, find an expression for the EMF as a function of time. (h) The horizontal component of the magnetic field B points north. Find approximate expressions for the time dependence of the signal seen by the shark when it is moving in a horizontal direction: north, south, cast, and west. (i) Comment on which directions result in the largest time dependence of the EMF. Is it possible to tell north from south or cast from west? Think about the fact that the shark knows both which direction its head is moving and the sign of V. (j) Why do you think that many aquatic vertebrates can sense electric fields, but very few terrestial vertebrates can?
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a The potential difference between the ends of the rod is given by the EMF equation EMF Bvl where v ... View the full answer
Related Book For
Accounting What the Numbers Mean
ISBN: 978-0078025297
10th edition
Authors: David H. Marshall, Wayne W. McManus, Daniel F. Viele
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