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A long straight wire is positioned in the plane of a conducting square loop of side A and resistance R. The wire is parallel to the closest side of the square loop and at a distance A from it. What is the average power dissipated in the loop when the current in the wire is I = I0sin(ωt).

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A. μ0/2π. Il㏒e. a+I/a. the average power dissipated in the loop is when the current in the wire is I = I0sin(ωt).

How to solve ?

As the field of current wire passing the loop is same in direction but not uniform in magnitude.

we use integration method for finding the flux.

The same flux ,a thin rectangular strip of length l and with dx, is given by

dϕB=Bx.dS=B(x)dScos180∘.

Magnetic field due to a long straight wire carrying current I is given by B=μ0I/2πx, and area, dS=l×dx.

∴ ϕB=∫dϕB=−∫μ0/2πIlx.dx=−μ0/2πIl[logex]x=a+l/x=a

=−μ0/2π.Illoge.a+I/a

How can I determine the average power lost by a resistor?

Any equation linking power to current, voltage, and resistance may be used to calculate the power wasted by each resistor because all three variables are known. Since each resistor receives its full voltage, let's use P=V2R P = V 2 R.

Power consumption and power dissipation are they equal?

Power consumption refers to the device's overall power usage. The portion of power used by objects unrelated to the targeted tasks is known as power dissipation.

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