016 (part 1 of 2) 10.0 points Consider two long parallel wires which are perpend

Question

016 (part 1 of 2) 10.0 points Consider two long parallel wires which are perpendicular to the plane of the paper (i.e., the r-y plane). Both wires carry the same current, I. wire #1 intersects the plane a distance a above point O and wire #2 inter- sects the plane a distance a below point O. Point C is equidistant from both wires and is a distance a from point O. 45° III IV wire #2 What is the direction of the magnetic field at D? 1. in the positive y direction 2. in the negative r direction 3. in quadrant I 4. in quadrant II 5. in quadrant IV 6. in the positive r direction 7. out of the plane 8. in the negative y direction

Explanation / Answer

magnetic field due to current carrying wire at a distance of d from the wire is B = mu_o*i/(2*pi*d)

at point D )

since thw two currents are in same direction,then

magnetic field is in same direction

by using right hand rule

we can say that net magnetic field is in the positive x direction

due to top wire B1 = mu_o*I/(2*pi*3a) = mu_o*I/(3*2*pi*a) = (1/3)*[(mu_o*I)/(2*pi*a)]

due to bottom wire B2 = mu_o*I/(2*pi*a)

B = B1+B2 = (1/3)[(mu_o*I)/(2*pi*a)] + (mu_o*I/(2*pi*a)

B = (mu_o*I/(2*pi*a))*((1/3)+1)

B = (4/3)*(mu_o*I/(2*pi*a)) = (2/3)*(mu_o*I/(pi*a))

so correct option is 6)

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