A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in the figure below. A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in the figure below.L.(a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: u.)(b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the magnitude of the emf (in V) that is induced in the loop if b = 18.0 A/s, h = 1.00 cm, w = 20.0 cm, and L = 1.30 m.(c) What is the direction of the induced current in the rectangle?O clockwiseO counterclockwiseO The magnitude is zero.What If? Suppose a constant current of I = 6.00 A flows in the straight wire and the loop moves from an initial position h, = 1.00 cm toward the bottom of the figure at a constant speed of v = 18.0 cm/s.(d) What is the magnitude of the induced emf (in V) in the loop 1.00 s after it begins to move?V(e) What is the direction of the induced current in the loop 1.00 s after it begins to move?O clockwiseO counterclockwiseO The magnitude is zero.

The magnetic field produced by a long straight wire at a perpendicular distance r from it is given as B=μoI2πrI is the current passing through the wire As can be seen, this magnetic field is inversely proportional to the distance from the wire, which means that the strength of the magnetic field decreases as the distance from the wire is increased. Now a loop in the form of a square is placed near this wire. So the loop will experience the magnetic field produced by this wire. But since the magnetic field is not uniform with distance, so different points on the square loop will experience different magnetic field strengths.To solve this problem, consider an infinitesimal segment of the square loop, having a small width equal to dr, and length L. Let this segment be at a distance r from the current carrying wire. The infinitesimal magnetic flux experienced by this segment due to the magnetic field of the wire is given as dϕ=B.dSdS is the area element of the segmentThis area element is given asdS=LdrThus,dϕ=BLdrdϕ=μoI2πrLdr From this, the magnetic flux over the entire loop of width w is given as ϕ=∮dϕϕ=∫μoI2πrLdr Since the wire is placed at a distance h from the loop, the limits of the above integral are written as ϕ=∫hw+hμoI2πrLdrϕ=μoIL2π∫hw+h1rdrϕ=μoIL2πlnrhw+hϕ=μoIL2πlnw+hh This is the expression for the magnetic flux over the entire square loopNow a time varying current is introduced in the long wire, which means that the magnetic field produced by this wire will also be a time varying field. Hence, the magnetic flux experienced by the square loop will also change over time, and this change in magnetic flux will induce an emf inside the loop, according to Faraday's law of electromagnetic induction. The time varying current is given as I=a+bt Thus, the flux becomes ϕ=μoIL2πlnw+hhϕ=μoa+btL2πlnw+hh Emf induced in the loop is given as e=dϕdte=ddtμoa+btL2πlnw+hhe=μoL2πlnw+hhddta+bte=μoL2πlnw+hhbFor the given constant values, b=18 A/s,h=1 cm=10-2 mw=20 cm= 0.2 mL=1.3 m e=μoL2πlnw+hhbe=4π×10-7×1.32πln0.2+10-210-218e=2.6×10-7ln21×18e=4.68×10-6×3.0445e=1.425×10-5 V This is the required value of the induced emfThe direction of this induced emf or induced current can be found using Lenz's law. This law states that the induced emf or current opposes the change in the flux producing it. In the given wire, the current is given as I=a+bt From this expression, it can be seen that with increasing time, the current in the wire increases, and as a result, magnetic field produced by this wire will also increase. This leads to an increase in flux through the square loop. Since this flux is increasing, the emf induced in this loop will act such as to oppose this increasing flux. The current induced in the loop will produce an induced magnetic field of its own. Since the flux and the magnetic field through the square loop is increasing, the induced magnetic field will act to reduce this increasing magnetic field, and thus will point in the opposite direction of the original magnetic field. The original magnetic field points into the plane of the figure. And so the direction of the induced magnetic field will have to be out of the plane of the figure. Thus, to produce a magnetic field in this direction, the direction of the induced current in the loop will have to be anticlockwise.Answers: Magnetic flux through the loop is ϕ=μoIL2πlnw+hh Emf induced in the loop is 1.425 x 10-5 V Direction of induced current is anti-clockwise Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered.

Answered: A loop of wire in the shape of a…