Question

Problem 3

The purpose of this problem is to find the Net Magnetic Field force of the two electric currents at point P.

There are two parallel wires carrying currents I₁ = 15 A and I₂ =25 A, as it is shown in the figure below. The arrow on each wire shows the direction of the current in the wire.

The distance between the two wires is 10 Cm. The distance between point P and the wire (I₁ ) on the left is 4 Cm.

1 Cm = 10^-2 m

Instruction:

            Solid blue circle indicates the direction of the electric current is out of the paper

           

         Solid blue circle with a cross sign indicates the direction of the electric current goes in to the paper.

I₁ = 15.0 A (solid blue) -------------------pX-------------------------------------------------------(solid blue w/cross) I₂ = 25.0

          

                                                                                                                                   

1. Calculate the magnetic field ( B1) of the left wire (I ₁ ) at point P. Show your formula and solution below this line.

B1 =

2. Calculate the magnetic field ( B2) of the right wire (I ₂ ) at point P. Show your formula and solution below this line.

B2 =

3. Draw the magnetic field vectors B1 and B2,   at point P, on the figure.

4. Calculate the net magnitude of the magnetic field , B(Net) and show the direction of the B(Net) at that point (P).

Answer 1

The equation to find magnetic field at any point is

B = u_oI / 2r

here r is the distance between wire and point where field is to be found

so,

(a) B₁ = 4e-7 * 15 / 2 * 0.14

B₁ = 2.1428e-5 T

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(b) B₂ = 4e-7 * 25 / 2 * 0.04

B₂ = 1.25e-4 T

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(c)

for solid blue circle, the direction of current is out of the page, so magnetic field at point P will be upwards.

for solid blue circle with cross, the direction of current is into the page, so magnetic field at point P will be downwards.

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(d) Now, we need to find total field, be careful with directions. we treat downward field as negative

B = B₁ -  B₂

B = 2.1428e-5 - 1.25e-4

B = - 1.0357e-4 T

negative sign means net magnetic field at point P points downward.