Point P is midway between two long, straight, parallelwires that run east west i

Question

Point P is midway between two long, straight, parallelwires that run east west in a horizontal plane. The distancebetween the wires is 0.8 cm. Each wirecarries a current of 0.8 A toward theeast. (a) Find the magnitude and direction of themagnetic field at point P. in T

(b) Repeat the question if the current in the wire on the southside runs toward the west instead. in T (a) Find the magnitude and direction of themagnetic field at point P. in T

(b) Repeat the question if the current in the wire on the southside runs toward the west instead. in T

Explanation / Answer

The distance between the wires is d = 0.8 cm = 0.8 *10-2 m The current carried by the two wires is I1=I2= 0.8 A (a)The magnitude of the magnetic field at point P due to thefirst wire is B1= (oI/2r)------------------(1) Here,o= 4 * 10-7NA-2,I = I1= 0.8 A and r = (d/2) = (0.8 *10-2/2) = 0.4 * 10-2 m Substituting the above values in equation (1),we get B1= (4 * 10-7 * 0.8/2 * 0.4* 10-2) = 8 * 10-5 T The magnitude of the magnetic field at point P due tothe second wire is B2= (oI/2r) Here,I = I2= 0.8 A or B2= (4 * 10-7 * 0.8/2 *0.4 * 10-2) = 8 * 10-5 T The magnitude of the resultant magnetic field at point Pis B = [B12 + B22 +2B1B2cos]1/2 Here, = 0o or B = [B12 + B22+2B1B2cos(0o)]1/2 or B = [B12 + B22+ 2B1B2] Substituting the values in the above equation,we get B = [(8 * 10-5)2 + (8 *10-5)2 + 2 * 8 * 10-5 * 8 *10-5]1/2 or B = [4 * (8 * 10-5)2]1/2 or B = 2 * 8 * 10-5 = 16 * 10-5 T According to the ampere's right hand thumb rule,if the thumbof the right hand points in the direction of the current then thecurling of fingers indicates the direction of the magneticfield.Therefore,when the current in the two wires is towards theeast then the magnetic field is out of the paper. (b)When the current in the wire on the south side runs towardthe west instead,then the direction of the magnetic field is intothe paper.The magnitude of the magnetic field is same as in part(a). or B = 2 * 8 * 10-5 = 16 * 10-5 T According to the ampere's right hand thumb rule,if the thumbof the right hand points in the direction of the current then thecurling of fingers indicates the direction of the magneticfield.Therefore,when the current in the two wires is towards theeast then the magnetic field is out of the paper. (b)When the current in the wire on the south side runs towardthe west instead,then the direction of the magnetic field is intothe paper.The magnitude of the magnetic field is same as in part(a).

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