Four very long, current-carrying wires in the same plane intersect to form a square with side lengths of 45.0 cm, as shown in the figure blelow.
Four very long, current-carrying wires in the same plane intersect to form a square with side lengths of 45.0 cm, as shown in the figure blelow. The currents running through the wires are 8.0 A, 20.0 A, 10.0 A, and I.  

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Part A  

Find the magnitude of the current I that will make the magnetic field at the center of the square equal to zero.  

Part B  

What is the direction of the current I (up or down)?
Solution


![image](https://q2a.s3.us-west-1.amazonaws.com/prod/answer-four-long-current-carrying-wires-planeintersect-form-square-side-lengths.jpeg)  

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the force on the wire due to the interaction of magnetic fields of the bar magnet and current carrying wire can act only in upwards or downwards direction. that depends on a lot of things. in particular, you would need to find the electric susceptibility of the paper. the field produced by static charge is inverse-square. the polarization of the paper varies directly with the external field, with a proportionality constant equal to the electric susceptibility. the dipole field created by the polarized paper is inverse-cube. overall, the force between the ruler and the paper will vary with the inverse fifth power of distance. to get any more detailed, you would need to know the geometry of the situation, and the charge distribution. (a) clockwise would be the direction of magnetic field in wire a.(b) the direction of the magnetic field in the wire b is anticlockwise.maxwell’s right hand thumb rule. answer: eddy currents are currents that circulate in conductors like swirling eddies in a stream. they are induced by changing magnetic fields and flow in closed loops, perpendicular to the plane of the magnetic field. they arise when a conductor moves through a magnetic field, or when the magnetic field surrounding a stationary conductor is varying. to summarise, we can say that anything which results in the conductor experiencing a change in the intensity or direction of a magnetic field produces eddy currents. the two uses of eddy current are: it is used in household current meters to measure power consumption. it is used to check whether the material or surface has any discontinuities, fractures, or faults without harming the material. what are the functions of a transformer? what is the working principle of a transformer? you don't say that the area must be a rectangle. the true largest area would be a circle, with the circumference equal to 400m and the area would be 12,732.4 m^2. however, evidently, the area is restricted to a rectangle, in which case the maximum area is a square, and the side of the square will be 
400/4 = 100 m. the area is 100x100 = 10,000 m^2.
algebraically,
let x = one pair of opposite sides
(400-2x)/2 = 200-x = the other pair of opposite sides

area = a(x) = x(200 - x) = -x^2 + 200x
x-coordinate of vertex = -b/2a = 200/2 = 100
a(100) = 10,000

that's it! ;) as the length of the wire increases so does the electrical resistance as electrons experience a smaller pd gradient as wire gets longer. the size of voltage per metre value decreases causing a lower drift velocity and more ions for electrons to collide with consider the parallelogram abcd with diagonals ac and bd as shown and they intersect at right angles at oa parallelogram is a square if its adjacent angles are 90° and adjacent sides are equalso we have to prove that adjacent sides of given parallelogram are equal and adjacent angles are 90° to prove given parallelogram is a squareconsider δbad and δcdaac = bd … givenab = dc … opposite sides of a parallelogramad is the common sidetherefore, δbad ≅ δcda … sss test for congruency⇒ ∠bad = ∠cda …corresponding angles of congruent triangles …(i)as it is given that abcd is parallelogram⇒ ∠bad + ∠cda = 180° … sum of adjacent angles of a parallelogram is 180°using equation (i)⇒ ∠cda + ∠cda = 180°⇒ 2 × ∠cda = 180°⇒ ∠cda = 90°⇒ ∠bad = 90°thus, adjacent angles are 90° … (iii)consider δaob and δaod∠aob = ∠aod … both 90° because given that diagonals intersect at right anglesod = ob … diagonals of a parallelogram bisect each otherao is the common sidetherefore, δaob ≅ δaod … sas test for congruency⇒ ab = ad … corresponding sides of congruent trianglesthus, adjacent sides are equal … (iv)from statements (iii) and (iv) we can conclude that parallelogram abcd is a squaretherefore, if in a parallelogram, the diagonals are equal in lengths and intersect at right angles, the parallelogram will be a square. the sides of the triangle are 6 cm, 8 cm and 10 cm. the longest side is 10 cm. (10)2 = 100 ….(i) now, the sum of the squares of the other two sides will be, (6)2 + (8)2 = 36 + 64 = 100 ….(ii) (10)2 = (6)2 + (8)2 ….. from (i) and (ii) by the converse of pythagoras theorem: the given sides form a right angled triangle. answer: 15
solution: there are six straight lines `l\_(1),l\_(2),l\_(3),l\_(4),l\_(5),l\_(6)` in a plane.   
 since no two lines are parallel and no three of which pass through the same point, we have maximum points of intersection.   
 line `l\_(1)` intersect five lines, so there will be five points of intersection.   
 similarly, for each of the lines `l\_(2),l\_(3),l\_(4),l\_(5),l\_(6)`, there will be five points of intersection.   
 but there will be double counting .   
 so, total number of points of intersection is `(5xx6)/(2)=15` from the figure:total resistance of the circuit, r = (rab + 15) ω = 20 ωcurrent in the circuit , \[i = \frac{v}{r} = \frac{8}{20} a\] ∴ voltage across ab, vab = i.rab = 2 vthe emf of the cell connected as above is given by: \[e = \frac{l}{l} v\_0\] here:l = 60 cm (balance point)ab = l = 1 m = 100 cm (total length of the wire) \[\therefore e = \frac{60}{100}\left( 2 \right) = 1 . 2 v\]