So, How to Use Ampere's Law for Magnetic Fields and Current?

[Maxwellkid]

I'm trying to find out which logical statement is true.

If and only if there is a region of space where there is no current, there cannot be a magnetic field that is both unidirectional and nonuniform.

Or

if there is a region of space where there is no current, there cannot be a magnetic field that is both unidirectional and nonuniform.

Which statement is true?

 

[berkeman]

I'm trying to find out which logical statement is true.

If and only if there is a region of space where there is no current, there cannot be a magnetic field that is both unidirectional and nonuniform.

Or

if there is a region of space where there is no current, there cannot be a magnetic field that is both unidirectional and nonuniform.

Which statement is true?

What is the context for the question? Is it for schoolwork?

What are the relevant equations for figuring this out? There are a couple of equations that relate current and magnetic field...

 

[Red_CCF]

I'm trying to find out which logical statement is true.

If and only if there is a region of space where there is no current, there cannot be a magnetic field that is both unidirectional and nonuniform.

Or

if there is a region of space where there is no current, there cannot be a magnetic field that is both unidirectional and nonuniform.

Which statement is true?

aren't these two statements exactly the same?

 

[Maxwellkid]

aren't these two statements exactly the same?

no, first statement is an equal sign. if and only if x then 5 means x=5

second statement is an if and then statement. if x then 5 doesn't mean x=5 because if 5 then x cannot be concluded.

2 statements are NOT logical the same.

 

[berkeman]

What is the context for the question? Is it for schoolwork?

What are the relevant equations for figuring this out? There are a couple of equations that relate current and magnetic field...

Any answers?

 

[Maxwellkid]

Any answers?

i'm using Ampere's law to investigate nonuniform unidirectional B fields.

 

[berkeman]

Cool. So can you show us how to use Ampere's Law to start go answer your questions?

 

[Maxwellkid]

Cool. So can you show us how to use Ampere's Law to start go answer your questions?

i would draw a rectangular dL with 2 sides of the rectangle parallel and antiparallel to nonuniform and unidirectional B field lines.

$$\oint \vec{B}\cdot \vec{dL} = \mu_{o} I_{enc}$$

where $$I_{enc} = 0$$