Static Electricity Legacy Problem #17 Guided Solution
Problem*
High voltage electrical cables generate an electric field in the region of space surrounding the cables. This field can be strong enough to cause a coronal glow in grounded objects and to ignite combustible fuels. According to one source, utility companies take measures to insure that the electrical field intensity is no greater than 1000 N/C at the perimeter of their public lands. Determine the force that would be experienced by a 1.0 μC charge when placed at this location.
Audio Guided Solution
The electric field intensity describes the amount of force on a quantity of charge which is placed at any given location where there is an electric field. We describe the electric field at a given location as being 1000 Newtons per Coulomb, and what we're saying is that for every 1 Coulomb of charge that's placed at that location, it will experience a force of 1000 Newtons. So here if we place a 1 micro Coulomb charge at a given location where there's 1000 Newtons per Coulomb electric field intensity, we should be able to calculate the amount of force on that micro Coulomb of charge. We need to use the equation that states that E, the electric field intensity, here 1000 Newtons per Coulomb, is equal to the force per quantity of charge, or F per Q. Here Q is 1.0 micro Coulombs, not a great unit when we have the electric field in Newtons per Coulomb, and so we need to convert the Q value, 1.0 micro Coulomb, to 1.0 times 10 to the negative 6 Coulombs. Now we can use some algebra to rearrange the equation to F equal E times Q. We can multiply the 1000 Newtons per Coulomb times the 1.0 times 10 to the negative 6 Coulombs, and we would get about 0.0010 Newtons of force at this location.
Solution
1.0x10-3 N or 0.0010 N
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities; record them in an organized manner. A diagram is a great place to record such information. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(Q_1 = 2.4 \unit{\micro\coulomb}\); \(Q_2 = 3.8 \unit{\micro\coulomb}\); \(d = 1.8 \unit{m}\); \(F_\text{elect} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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