Question

In: Physics

The unit of current, the ampere, is defined in terms of the force between currents. Two...

The unit of current, the ampere, is defined in terms of the force between currents. Two 1.0-meter-long sections of very long wires a distance 2.0m apart each carry a current of 1.0 A

What is the force between them? (If the force between two actual wires has this value, the current is defined to be exactly 1 A.)

Solutions

Expert Solution

Concepts and reason

The concepts required to solve the given problem is magnetic field due to a current carrying wire and force on a current carrying wire due to magnetic field.

Initially, determine the magnetic field at one wire due to other wire by using expression magnetic field due to a current carrying wire. Then, determine the force on the wire by using magnetic field, length of the wire and current in the wire.

Fundamentals

The current carrying wire creates a magnetic field around the wire and the direction of magnetic field around the wire is known by using right hand rule.

The magnitude of magnetic field B due to a current carrying wire at distance r from the wire is given by following expression.

B=μ0I2πrB = \frac{{{\mu _0}I}}{{2\pi r}}

Here, I is the current, and μ0{\mu _0} is the permeability.

The magnetic force F on a current carrying wire is given by following expression.

F=BILF = BIL

Here, L is the length of the wire.

The magnitude of magnetic field B due to a current carrying wire at distance r from the wire is given by following expression.

B=μ0I2πrB = \frac{{{\mu _0}I}}{{2\pi r}}

Substitute 1.0 A for I, 2.0 for r, and 4π×107H/m4\pi \times {10^{ - 7}}\;{\rm{H/m}} for μ0{\mu _0} in the above equation.

B=(4π×107H/m)(1.0A)2π(2.0m)=1×107T\begin{array}{c}\\B = \frac{{\left( {4\pi \times {{10}^{ - 7}}\;{\rm{H/m}}} \right)\left( {1.0\;{\rm{A}}} \right)}}{{2\pi \left( {2.0\,{\rm{m}}} \right)}}\\\\ = 1 \times {10^{ - 7}}\,{\rm{T}}\\\end{array}

The magnetic force F on a current carrying wire is,

F=BILF = BIL

Substitute 1.0 A for I, 1×107T1 \times {10^{ - 7}}\,{\rm{T}} for B, and 1.0 m for L in the above equation.

F=(1×107T)(1.0A)(1.0m)=1×107N\begin{array}{c}\\F = \left( {1 \times {{10}^{ - 7}}\,{\rm{T}}} \right)\left( {1.0\,{\rm{A}}} \right)\left( {1.0\,{\rm{m}}} \right)\\\\ = 1 \times {10^{ - 7}}\,{\rm{N}}\\\end{array}

Ans:

The force between the wires is 1×107N.1 \times {10^{ - 7}}\,{\rm{N}}{\rm{.}}


Related Solutions

Two stacked rings have currents in opposite directions as shown. There is a net magnetic force...
Two stacked rings have currents in opposite directions as shown. There is a net magnetic force exerted on the top ring due to the bottom ring. Is which direction is this force? to the right to the left downward upward The net force is zero.
What is the magnitude of the force per unit area between two infinite, uniformly charged plates...
What is the magnitude of the force per unit area between two infinite, uniformly charged plates with a surface charge density of +4.20
Distinguish between the constructs of intelligence and achievement in terms of how they are defined and...
Distinguish between the constructs of intelligence and achievement in terms of how they are defined and how they are measured. In what ways could these constructs be used to create a theoretical framework for research? Support your answer.
Two current carrying wires carry currents of 4A and 3A. Calculate the magnetic field at point...
Two current carrying wires carry currents of 4A and 3A. Calculate the magnetic field at point P
Question 1 Stress is defined as 1. Force x Area 2. Force - Area 3. Force...
Question 1 Stress is defined as 1. Force x Area 2. Force - Area 3. Force + Area 4. Force/Area 10 points Question 2 Stress value below the earth surface depends on: 1. Density of soil particles 2. Depth of the point at consideration 3. Both 1 and 2 4. None of the answers 10 points Question 3 Neutral Stress results from: 1. Soil particles 2. Seismic activity 3. Both water and soil 4. Water table 10 points Question 4...
Design an experiment to find the relationship between the electric force between the two spheres and...
Design an experiment to find the relationship between the electric force between the two spheres and the distance between them. In the space below, describe your experiment, including: What quantity did you vary? What quantities did you hold constant? What quantity did you measure? Which quantities did you plot on your graph, and on which axes? Which Curve Fit gives the best fit for the data? Describe your process and the relationship you found. In particular, note where the data...
briefly explain the relationship between these two terms.
Business and Ecology are two different terms; briefly explain the relationship between these two terms.
Two long, parallel wires are separated by a distance of 3.80 cm. The force per unit...
Two long, parallel wires are separated by a distance of 3.80 cm. The force per unit length that each wire exerts on the other is 3.80×10−5 N/m, and the wires repel each other. The current in one wire is 0.600 A. What is the current in the second wire? Express your answer in amperes. Are the two currents in the same direction or in opposite directions?
5- how are the resistor currents related to the circuit current? 6- How are the resistor...
5- how are the resistor currents related to the circuit current? 6- How are the resistor currents and resistances related? 7- how are the currents in the wires related to the currents in the resistors ? 8- what can you conclude about Currents in a series circuit? Is the circuit current the same as it was in the parallels circuit?why?
Use the current-voltage equation for the Na+ and K+ currents to derive the GHK equation for...
Use the current-voltage equation for the Na+ and K+ currents to derive the GHK equation for the reversal potential for a channel permeable to both Na+ and K+.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT