4. A squre coil of wire with 800 turns and size a = 10.0 cm on each side, is held next to a long straight wire whichcarries a time varying current I(t) = 9x10* e-0.08t Amperes. Assume the center of the coil is 102.0 cm away fromthe wire and the coil and the wire are in the same plane.a) What is the value and direction of the B field, due to current in the straight wire, at the center of the coil (asa function of time)?b) Calculate the flux of this B-field through the coil (as a function of time). Assume the B field is uniforminside the coil, because coil is small and far from wire.c) Use the Faraday's law to determine the generated EMF (as a function of time) in the coil.d) If the resistance of the coil is R=20 2, what is the torque acting on the coil at time t ?e) What is the potential energy of the coil at time t ?f) Answer (d) and (e), if the coil is now at an angle of 0 with respect to vertical.Coila

Note-Since we only answer up to 3 sub-parts, we will answer the first 3. Please resubmit the question and specify the other sub-parts (up to 3) you'd like answered. N=800 , a=10 cm, I(t)=9×104 e-0.08t Amperes, distance of center of loop and wire, x=102 cm (a) The magnetic field at the center of the loop can be calculated by the formula B(t)=μ0 I(t)2πx and the direction will be outward normal of the loop. Substituting the values in the above equation we get B(t)=4π×10-7 ×9×104 ×e-0.08t2×π×1.02 or, B(t)=0.0176 e-0.08t Tesla(b) Since magnetic field is uniform over the entire loop we will take value of field at center as value of field in entire loop. The area vector of the loop is also along the outward normal of the diagram. Thus, ϕ(t)= N B→ (t).ds→ where A→ is area vector of the loop. The direction of magnetic field and the area vector is same that is angle between them is zero degree. So we can write, ϕ(t)=N B(t) A cos0 or, ϕ(t)=N B(t) A Putting the values of magnetic field and area we get, ϕ(t)=800×0.0176 e-0.08t ×0.1×0.1 ϕ(t)=0.1408 e-0.08t weber(c) From Faraday's law we know that induced emf is given by, ε=-dϕ(t)dt or, ε=-0.1408 d e-0.08tdt or, ε=-0.1408×-0.08×e-0.08t or ε=0.0112 e-0.08t volts

Answered: 4. A squre coil of wire with 800 turns…