Question

A magnetic field of magnitude 0.270 T is oriented perpendicular to the plane of a circular loop. HINT (a) Calculate the loop radius (in m) if the magnetic flux through the loop is 2.25 Wb. 1.62 Correct: Your answer is correct. The SI unit of magnetic flux is the weber (Wb), given by 1 Wb = 1 T · m2. m (b) Calculate the new magnetic flux (in Wb) if the loop radius is doubled. 4 Incorrect: Your answer is incorrect. Wb

Answer 1

(a) 1.63 m

(b) 9.01 Wb

Step-by-step explanation:

Parameters given:

Magnetic field, B = 0.27 T

(a) Magnetic flux is the product of magnetic field and Area of a coil. It is given mathematically as:

∅ = BA

where A = area of coil =
`\pi r^2`

=> ∅ = B
`\pi r^2`

Making r subject of formula, we have:

`r^2` = ∅/(Bπ)

When ∅ = 2.25 Wb:

`r^2` =
`(2.25)/(0.27 * \pi )`

`r^2` =
`2.653`

`r = √(2.653)` =
`1.63 m`

(b) If the radius is doubled, r = 1.63 * 2 = 3.26 m. Then, the magnetic flux will be:

∅ = BA = B
`\pi r^2`

∅ = 0.27 * π *
`3.26^2`

∅ = 9.01 Wb