# Ampere definition and infinite wires separated by 1 meter

## Homework Statement

3 - 2 , 1 km wires ( so acting like infinite wires ) , both have same current , no direction specified , , separated by 1 meter distance and having between them a magnetic force of module 0.02 N .
find the current i=

## Homework Equations

the definition of 1 ampere has same conditions except the force between should be 2*10^-7 ,

## The Attempt at a Solution

0.02 N is 2 *10^-2 so this is 100000 times bigger than 1 amp ?

or other way around , 1/100000 amps ?

im positive this can be solve using symetry and the ampere definition ,

## Answers and Replies

kuruman
Science Advisor
Homework Helper
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What is an expression for the force between the wires in terms of the current and the separation?

theres few name for this formula ,

F (b<-a) = ibL X Ba so a vector product

which if both are orthogonal , we can rewrite as F(b<-a) = ib LBa sine 90 = ibLBa = u0Liaib / 2pid

Ba = u0ia / 2 pid

if we analyze the formula we find we have the constant u0 = 4pi*10^-7
we also find the expression 2pi , so the variables are the current i and the distance d for the magnetic field and for the force .

so , since every distance value has a symetric axis, and every number has a symetric axis .

this kind of problem can be answered by symetric deduction .

or we can use the formula :) but by symetric deduction the answer would be either 0..01 or the 2 i rtied earlier in the post

kuruman
Science Advisor
Homework Helper
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the definition of 1 ampere has same conditions except the force between should be 2*10^-7 ,

## The Attempt at a Solution

0.02 N is 2 *10^-2 so this is 100000 times bigger than 1 amp ?

or other way around , 1/100000 amps ?

im positive this can be solve using symetry and the ampere definition ,
Yes, this can be solved using the ampere definition if you know what you're doing. You still need an equation for the force between the wires to look at.
Here, the force between the given wires is 105 times larger than in the definition while the separation is the same.
Question 1: To get a larger force do you need more or less current than 1 A?
Question 2: Does the force depend linearly on the current or not?

the equation does have a lenght vector L
the force felt by b from the a wire has formula ibL ^ Ba the variables influencing the force are the current and distance . higher the distance , smaller the force .
higher the current , higher the force ,
no?

answer cant be 100 000 amps... and 0.01 seems too easy for it to be the answer

Last edited:
kuruman
Science Advisor
Homework Helper
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the equation does have a lenght vector L
the force felt by b from the a wire has formula ibL ^ Ba the variables influencing the force are the current and distance . higher the distance , smaller the force .
higher the current , higher the force ,
no?

answer cant be 100 000 amps... and 0.01 seems too easy for it to be the answer
Yes, the higher the distance the smaller the force and the higher the current the higher the force.
You did not really answer question 2 in post #4. Please answer it. It would help if if you wrote down an equation for the force "felt by b from the a wire". What you have, ibL^Ba, is not an equation. Also, what is Ba in terms of the given quantities and the usual constants? You need to put that in. Don't try to do this problem in your head.

well the problem stated here is quite vague , and here are the formulas found in the book, for a force between 2 parallele current can either be attractive or repulsive depending if the current is oriented in the same direction . So i gather the amount of force is the same , with only the sign changing if its a repulsive force or attractive force .

Ba norm of magnetic field made by the a wire = μ0 ia
2πd
ib = current in b wire
ia = current in a wire

Force on b from a = ibL X Ba ( current from b wire , * lenght vector ) cross product with the magnetic field of b wire
Force on b from a = ibLBasine90 = μ0Liaib
2πd

B= (μ0 /4π) * (dℓ×r ) /r^2. which is biot savart law .

or the formula for lorentz force , which i dont think is the issue here

the current is the same everywhere in the wire , so the force should be the same everywhere in the wire for 2 points a b at the same distance

in french we say depends linearly when the graph of it would be a straight line . but here in french we woud say inversely proportional if force depends on 1/r
so in french we say the force is proportional to the current— double the
current in one of the wires, and you double the force.
Double the current in both wires, and you quadruple the force., so we have force by unit lenght F/L = (I/c)ˆn × B.

F/L= μ0 I1 I2 / 2πr, but these formulas arent in my book
.

kuruman
Science Advisor
Homework Helper
Gold Member
F/L= μ0 I1 I2 / 2πr, but these formulas arent in my book
.
Books don't have all the formulas. They have the important ones so that you, using a bit of algebra, can put them together to get whatever formula is appropriate to your problem. Can you answer the question now?

(2*10^-2) N / 1000metre= ((4π*10^-7) i ^2 ) / 2π *1 or * 0.5 ) since distance between the wire is 1 metre . so diameter is 1 meter , r should be half that, so 0.5

so if r =1 and L = 1000 meters ---> i = 10 amps
if r=1 and no value for L then i = 316 amps
if r= 0.5 and L= 1000 meters i = 7.071 amps
if r=0.5 and no value for L used then i = 223 amps

by fiddling with the amp definition and what u said in previous post, i also got i = 20 amps . but the 10 amps gotten by using r=1 and L =1000 , looks like a good answers , it has symetry with the question statement so

10 amps ?