(a) What is the direction of the force on a wire carrying a current due east in a location where the Earth’s field is due north? Both are parallel to the ground.
Answer: Direction of force is Vertically up from ground
(b) Calculate the force per meter if the wire carries 23.0 A and the field strength is 2.88×10-5 T.
(c) What diameter copper wire would have its weight supported by this force?
(d) Calculate the resistance per meter and the voltage per meter needed.
I answered the first question, but not sure how to answer the other three
(b) To calculate the force per meter, we can use the formula:
Force per meter (F) = Current (I) * Magnetic Field Strength (B)
Given that the current is 23.0 A and the field strength is 2.88×10-5 T, we can substitute these values into the formula:
F = 23.0 A * 2.88×10-5 T
Solve the multiplication to find the force per meter.
(c) To determine the diameter of the copper wire that would have its weight supported by this force, we need to consider the relationship between force, weight, and area. The force per meter acting on the wire is equal to the weight per meter. And the weight of an object is given by the equation:
Weight = Mass * Gravitational Acceleration
Since we want the force per meter to support the weight, we set the force per meter equal to the weight per meter.
Force per meter = Weight per meter
We can rearrange this equation to solve for the weight per meter.
Weight per meter = Force per meter
Now, we can use the weight per meter to calculate the weight of the wire, knowing the formula:
Weight = Volume * Density * Gravitational Acceleration
Since we have the weight and the density of copper, we can rearrange the equation to solve for the volume.
Volume = Weight / (Density * Gravitational Acceleration)
Finally, we can calculate the diameter of the wire using the formula:
Volume = (pi/4) * (Diameter)^2 * Length
Where Length is the length of the wire.
(d) To calculate the resistance per meter, we can use the formula:
Resistance per meter = Resistivity * Length / Area
Where Length is the length of the wire and Resistivity is a property of the material used. For copper, the resistivity is approximately 1.7 x 10^-8 Ω·m.
To calculate the voltage per meter, we can use Ohm's Law:
Voltage per meter = Current * Resistance per meter
Substitute the given values of current and resistance per meter into the formula to find the voltage per meter.