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Determining an expression for the magnitude and direction of a magnetic field

Please show all the work.

Problem #1: A closed section of a wire in the shape shown in bold in the figure (attached) carries a uniform current I counterclockwise. This section of wire lies completely in the plane of the paper.

The figure consists of three-quarters of a circle of radius R and two straight lines, both of length R. Determine an expression for the magnitude and direction of the magnetic field at the point P (small circle) indicated in the figure.

Your final answer should be in terms of just mu0, I and R.

Problem #2: Three long wires carry currents I1, I2 and I3 with I1 coming perpendicularly out of the page through the point (-a,0), I2 going perpendicularly into the page through the point (0,0), and I3 coming perpendicularly out of the page through the point (+a,0). A fourth long wire carries a current I and passes perpendicularly through the page at the point (+a,+b). If I2 = 50 A, a = 3 m and b = 4 m, determine I1 and I3 so that the total magnetostatic force on I due to I1, I2 and I3 is zero.

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Please refer to the attachment.
Solution #1:

B

O R C
R 45O I
45O
A D
Net magnetic field at the centre O is the vector sum of the magnetic fields due to three sections viz. ¾ circle CBA of radius R, straight wires AD and DC. We determine below the magnetic field vectors due to each of these sections.
Magnetic field due to CBA
Magnetic field due to a current carrying loop of radius R at its centre is given by: B = μoI/2R
Magnetic field at O due to ¾ of the circular loop is given by: BCBA = ¾ x (μoI/2R) = 3μoI/8R ....(1)
Direction of this magnetic field is out of the plane (curl the fingers of the right hand in the ...

Solution Summary

An expressions for the magnitudes and direction of a magnetic fields.

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