The four wires that lie at the corners of a square of side a= 4.20 cm are carryi

ID: 1374979 • Letter: T

Question

The four wires that lie at the corners of a square of side a= 4.20 cm are carrying equal currents i= 2.40 A into (+) or out of (-) the page, as shown in the picture.

1. Calculate the y component of the magnetic field at the center of the square.

HINT:

2. Calculate the x-component of the force on a 1.0-cm long piece of the lower right-hand wire, due to the other three wires.

Use the right-hand rule to get the field of each wire at the origin. Determine the y-components of each of these field vectors. Use the superposition principle to get the total field and its y-component. The four wires that lie at the corners of a square of side a= 4.20 cm are carrying equal currents i= 2.40 A into (+) or out of (-) the page, as shown in the picture. 1. Calculate the y component of the magnetic field at the center of the square. HINT: Use the right-hand rule to get the field of each wire at the origin. Determine the y-components of each of these field vectors. Use the superposition principle to get the total field and its y-component. 2. Calculate the x-component of the force on a 1.0-cm long piece of the lower right-hand wire, due to the other three wires.

Explanation / Answer

Use F = I*L*B

now we need B on the lower rt wire (Note B = ?0*I/2?r but ?0/2? = 2x10^-7)

Now the lower - wire produces a field that is down and = 2x10^-7*2.40A/0.0420 = 1.143x10^-5T

the + wire produces the same field but is directed to the rt

the other - wire has a distance = 0.0420*cos(45) = .0297m

B = 2x10^-7*2.40/0.0297 = 1.616x10^-5T but this is directed down and to the left (45o)

Now the components are Bx = 1.143x10^-5T - 1.616x10^-5*cos(45) = 3.154x10^-9T

the y component is down =1.143x10^-5T+1.616x10^-5*cos(45) = 2.285x10^-5T

Since you only want the x component of the force then we only need the By component

Since I is out and B is down the resulting force will be in the +x direction

F = I*L*B =2.40*0.01*2.285x10^-5 =5.484x10^-7N

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