A current I flows through an infinitely long conductor ABC bent to form a right angle (Fig.).
How many times will the intensity of the magnetic field change at point M if an infinitely long straight conductor BD is so connected to point B that the current I branches at point B into two equal parts and the current in the conductor AB remains the same?
Text Solution
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Sol. The conductor BC does not induce a field at point M lying on the continuation of BC. According to the rule given in the note, the magnetic field produced by any elements of conductor BC should be perpendicular to line BM. For this reason the presence of field other than zero at point M would disagree with the symmetry of the problem, because all the directions perpendicular to BM have equal rights.
Since the intensity of the field is proportional to the current, then H 1 = kI without conductor BD. The fields from the conductors AB and BD are summated. Therefore after conductor BD is connected
H 2 = kI + 
whence 
= 
.
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