course Phys 202 8:49 PM 10-17-09 024.
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Given Solution: `aSTUDENT RESPONSE AND INSTRUCTOR COMMENT: electric field is the concentration of the electrical force ** That's a pretty good way to put it. Very specifically electric field measures the magnitude and direction of the electrical force, per unit of charge, that would be experienced by a charge placed at a given point. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: ok ********************************************* Question: `qQuery Principles of Physics and General Physics problem 16.15 charges 6 microC on diagonal corners, -6 microC on other diagonal corners of 1 m square; force on each. What is the magnitude and direction of the force on the positive charge at the lower left-hand corner? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Force = k q1q2/r^2 If corners are labeled as follows: 1= top left corner, 2 = bottom left, 3 = top right, and 4 = bottom right Force at bottom left corner (2): Need to get the Fx1 value and the Fy1 value Fx1 = F2,4 + F2,3x K (q2)(q4)/r^2 + k (q2)(q3)cos(theta) (9*10^9 Nm^2/C^2)(-6*10^-6 C)( 6*10^-6 C)/(1m)^2 + (9*10^9 Nm^2/C^2)(-6*10^-6 C)( 6*10^-6 C)/(1.41m)^2 cos(45 degrees) Note: a^2 + b^2 = c^2 1 m ^2 + 1 m^2 = c ^ 2 c= 1.41 m (distance from 2 to 3) -0.324 N + -0.115 N = -0.209 N Fy1 = F2,4 + F2,3y K (q2)(q4)/r^2 + k (q2)(q3)cos(theta) (9*10^9 Nm^2/C^2)(-6*10^-6 C)( 6*10^-6 C)/(1m)^2 + (9*10^9 Nm^2/C^2)(-6*10^-6 C)( 6*10^-6 C)/(1.41m)^2 sin(45 degrees) -0.324 N + -0.115 N = -0.209 N F = square root (Fx^2 + Fy^2) F = square root (-.209^2 + -.209^2) = 0.296 N Tan(theta) = Fy/Fx Tan (theta) = -.209/-.209 = 45 degrees confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** The charges which lie 1 meter apart are unlike and therefore exert attractive forces; these forces are each .324 Newtons. This is calculated using Coulomb's Law: F = 9 * 10^9 N m^2/C^2 * ( 6 * 10^-6 C) * ( 6 * 10^-6 C) / ( 1 m)^2 = 324 * 10^-3 N = .324 N. Charges across a diagonal are like and separated by `sqrt(2) meters = 1.414 meters, approx, and exert repulsive forces of .162 Newtons. This repulsive force is calculated using Coulomb's Law: F = 9 * 10^9 N m^2/C^2 * ( 6 * 10^-6 C) * ( 6* 10^-6 C) / ( 1.414 m)^2 = 162 * 10^-3 N = .162 N. The charge at the lower left-hand corner therefore experiences a force of .324 Newtons to the right, a force of .324 Newtons straight upward and a force of .162 Newtons at 45 deg down and to the left (at angle 225 deg with respect to the standard positive x axis, which we take as directed toward the right). This latter force has components Fy = .162 N sin(225 deg) = -.115 N, approx, and Fx = .162 N cos(225 deg) = -.115 N. The total force in the x direction is therefore -.115 N + .324 N = .21 N, approx; the total force in the y direction is -.115 N + .324 N = .21 N, approx. Thus the net force has magnitude `sqrt( (.21 N)^2 + (.21 N)^2) = .29 N at an angle of tan^-1( .21 N / .21 N) = tan^-1(1) = 45 deg. The magnitude and direction of the force on the negative charge at the lower right-hand corner is obtained by a similar analysis, which would show that this charge experiences forces of .324 N to the left, .324 N straight up, and .162 N down and to the right. The net force is found by standard vector methods to be about .29 N up and to the left. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `qquery university physics 21.68 (22.52 10th edition) 5 nC at the origin, -2 nC at (4 cm, 0). If 6 nC are placed at (4cm, 3cm), what are the components of the resulting force? ********************************************* Question: `qQuery univ phy 21.76 (10th edition 22.60) quadrupole (q at (0,a), (0, -a), -2q at origin). For y > a what is the magnitude and direction of the electric field at (0, y)? ********************************************* Question: `qquery univ 22.102 annulus in yz plane inner radius R1 outer R2, charge density `sigma.What is a total electric charge on the annulus? "