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Two parallel wires are 5.00 cm apart and carry currents in opposite directions, as shown in Fig. E28.12. Find the magnitude and direction of the magnetic field at point P due to two 1.50-mm segments of wire that are opposite each other and each 8.00 cm from P.

Short Answer

Expert verified

The magnetic field at point P due to two 1.50 mm segments isdBtot=2.64×10-7T

Step by step solution

01

Biot savart law

Consider the two parallel wires which are 5.00 cm apart and carry currents in opposition directions. We need to find the magnitude and direction field at point P which at distance 2.50cm from each one of the two-wire due to two segments of wire that are opposite each other and each r = 8.00cm from the point P .The magnetic field due to a segment of length dl and current of I is given by Biot Savart law as:

dB=μ04πldlsinϕr2

02

field at the point P

When theϕ angle between the position of unit vector and the length of the segment, as shown in the textbook figure this angle is the angle that the dotted line makes with the horizontal axis, we can see from the figure that thesinϕ=2.50cm/8.00cm . The magnetic field due to the two segments is into the page. Now, the magnetic field due to these segments at the point P will be:

dBtot=μ04πldlsinϕr2+μ04πldlsinϕr2

Now, the current differs in the two wires as:

dBtot=mu04πldlsinϕr2l1+l2

Now putting the values, we get:

2.64×10-7T

Which the magnetic field at the point.

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