Question

A loop of wire with radius r=0.071 m is in a magnetic field with magnitude B.B changes from B1=0.43 T to B2=8.5 T in t=7.5 s at a constant rate.Randomized Variablesr=0.071 mB1=0.43 TB2=8.5 TΔt=7.5s a. Express the magnetic flux Φ going through a loop of radius r assuming a constant magnetic field B,b. Express the change in the magnetic flux going through this loop, ΔΦ, in terms of B1,B21,2 and r,c. Calculate the numerical value of ΔΦ in T⋅m2,d. Express the magnitude of the average induced electric field, E, induced in the loop in terms of ΔΦ,r,, and Δt,e. Calculate the numerical value of E in N/C.

Answer 1

a. The magnetic flux Φ going through a loop of radius r assuming a constant magnetic field B is given by:

Φ = Bπr²

b. The change in magnetic flux going through the loop, ΔΦ, in terms of B1, B2, r is given by:

ΔΦ = Φ2 - Φ1 = B2πr² - B1πr² = πr²(B2 - B1)

c. Plugging in the values, we get:

ΔΦ = π(0.071 m)²(8.5 T - 0.43 T) ≈ 0.16 T⋅m²

d. The magnitude of the average induced electric field E induced in the loop in terms of ΔΦ, r, and Δt is given by:

E = ΔΦ / (rΔt)

Plugging in the values, we get:

E = (0.16 T⋅m²) / (0.071 m × 7.5 s) ≈ 0.296 N/C

Therefore, the numerical value of E is approximately 0.296 N/C.