A long current-carrying wire, oriented North-South, lies on a table (it is conne

Question

A long current-carrying wire, oriented North-South, lies on a table (it is connected to batteries which are not shown). A compass lies on top of the wire, with the compass needle about 3 mm above the wire. With the current running, the compass deflects 16 degrees to the West. At this location, the horizontal component of the Earth's magnetic field is about 2e-5 tesla.

A long current-carrying wire, oriented North-South, lies on a table (it is connected to batteries which are not shown). A compass lies on top of the wire, with the compass needle about 3 mm above the wire. With the current running, the compass deflects 16 degrees to the West. At this location, the horizontal component of the Earth's magnetic field is about 2e-5 tesla. What is the magnitude of the magnetic field at location A, on the table top, a distance 2.6 cm to the East of the wire, due only to the current in the wire? What is the direction of the magnetic field at location A, due only to the current in the wire?

Explanation / Answer

X=theta

tan(x)=B/Be

B=Betan(x)

since B=uoI/2pir

uoI/2pir =Be*tanx

uoI/2pi =Be*r*tanx

magnetic field at location A is

BA =uoI/2pid

BA =Be*r*tanx/d

BA =(2*10^-5)*(3*10^-3)*tan16/(2.6*10^-2)

BA=6.62*10^-7 T ot 0.662 uT

and direction is towardsup

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