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Thank you We sneak and here's your shmoop dues You

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are more to buy the queen of england Because being

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royalty is everyone's first career choice All right well check

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out falling diagram It shows two wires used in the

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cables placed parallel to one another and separated by a

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distance of feet Wire one carries a current of i

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sub one and wire to carries a current of ice

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up to the current ice of one equals one sixth

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of ice up to and the distance labeled x equals

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one fourth of the distance D find the magnitude and

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direction of the magnetic field Be savaii at point a

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and here the potential answer right there First of all

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let's figure out the direction of the field A magnetic

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field is in three dimensions but the screen were looking

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at on Lee has to it's like the page of

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a book So to determine how the field is turning

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around the wire will use a version of the right

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hand room Well look at the wire one first that

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current is moving Prop words So with an open hand

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we point the thumb of our right hand in the

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direction of the current Then we curl our fingers like

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we're making a furious physics fist of justice The direction

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that our fingers curl is the direction of the field

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Conventionally speaking of far fingers curl away from us The

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field is said to go into the page If the

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fingers curl toward us the field is said to go

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out of the page so the field around the first

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wire is going into the page for wire to our

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thumbs point down And once again our fingers curl away

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from us into the page since both fields or going

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in the same direction that combined field That point is

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also headed into the page so we can already not

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answers being deep out of contention And because the fields

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generated by each wire are in the same direction we

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can add them up to determine the total field at

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point a So now if we may let's get ready

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for equations Well the equation for magnitude for a magnetic

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field is the concept of permeability of free space times

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the current over to pi times the radius or the

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distance from the wire Well the equation looks like this

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Her point a the distance will use for the first

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wire is x and we'll use d minus x for

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the second wire When we adam together it looks like

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this and we could make that a little cleaner So

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now our equation is the constant of permeability of free

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space over to pi times the sum of current one

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over distance x plus current to over distance D minus

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x We can sub in the given value of Acts

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which was 1 quarter d to give us this equation

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And we can make that a little cleaner that way

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And we can also swap out current i sub one

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for its value in terms of ice Up to the

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field at point a equals the concept of permeability of

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free space over to pi times distance times the sum

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of four Six i sub two plus four thirds aye

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sub too And that equals the concept of permeability of

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free space Times ice up to over pi times distance

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at long last we can definitively say without a doubt

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the correct answer is c And after all that well 00:03:08.69 --> [endTime] we've got to go lay down

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