You are working in a biology lab during your summer break. Your supervisor asks you to perform an experiment to find the effective spring constant (in N/m) of a partial molecule of DNA (deoxyribonucleic acid). You perform experiments and find that a single straight portion of a DNA molecule is 2.32 µm long. You then perform an activity that charges the ends of the molecule; each end becomes singly ionized: negative on one end, positive on the other. After the ends are charged, the molecule shrinks by 1.25% of its length. Use the particle in equilibrium model to balance the electric and elastic forces on a particle at one of the ends of the molecule. N/m

You are working in a biology lab during your summer break. Your supervisor asks you to perform an experiment to find the effective spring constant (in N/m) of a partial molecule of DNA (deoxyribonucleic acid). You perform experiments and find that a single straight portion of a DNA molecule is 2.32 µm long. You then perform an activity that charges the ends of the molecule; each end becomes singly ionized: negative on one end, positive on the other. After the ends are charged, the molecule shrinks by 1.25% of its length. Use the particle in equilibrium model to balance the electric and elastic forces on a particle at one of the ends of the molecule. N/m

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter26: Electric Potential

Section: Chapter Questions

Problem 76PQ: An electric potential exists in a region of space such that V = 8x4 2y2 + 9z3 and V is in units of...

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A potential difference AV exists between the inner and outer surfaces of the membrane of a cell. The inner surface is negative relative to the outer surface. If 1.50 × 10-20 J of work is required to eject a positive potassium ion (K*) from the interior of the cell, what is the magnitude of the potential difference (in millivolts) between the inner and outer surfaces of the cell? |AV| = mV
You are working in a laboratory, using very sensitive measurement equipment. Your supervisor has explained that the equipment is also very sensitive to electrical discharge from human operators. Specification tables for the equipment indicate that an electrical discharge providing even a very small amount of energy of 250 μJ is enough to damage the equipment. Your supervisor wants to install an apparatus that will be used to remove the electrical charge from individuals’ bodies before they touch the equipment. To do this, she asks you to estimate (a) the capacitance of the human body and determine (b) the charge on the body and (c) the electric potential of the body, relative to a point infinitely far away, corresponding to the energy transfer that will damage the equipment.
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A Geiger-Mueller tube is a radiation detector that consists of a closed, hollow, metal cylinder (the cathode) of inner radius ra and a coaxial cylindrical wire (the anode) of radius rb (see figure below) with a gas filling the space between the electrodes. Assume that the internal diameter of a Geiger-Mueller tube is 1.95 cm and that the wire along the axis has a diameter of 0.210 mm. The dielectric strength of the gas between the central wire and the cylinder is 1.30 106 V/m. Use the equation 2?rℓE =qin/?0 to calculate the maximum potential difference that can be applied between the wire and the cylinder before breakdown occurs in the gas. [Image] A cross-section of a Geiger-Mueller tube shows an inner anode of radius rb and charge density ? and an outer cathode of radius ra and charge density −?.
Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius ry has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = aer/a0 + B/r + bo where alpha (a), beta (8), an and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vah between the two conductors. The potential difference is related to the electric field by: Vah = Edr= - Fdr Calculating the antiderivative or indefinite integral, Vab = (-aager/a0 +8 + bo By definition, the capacitance Cis related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C= Q/( (e"b/a0 .eralao) + B In( )+ bo ( ))
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