Question

Two generators use the same magnetic field and operate at the same frequency. Each has a single-turn circular coil. One generator has a coil radius of 5.1 cm and a peak emf of 1.8 V. The other generator has a peak emf of 3.9 V. Find the coil radius r of this other generator.

Answer 1

The radius of the second coil will be 7.5 cm

Step-by-step explanation:

We have given that radius of the first coil
`r_1=5.1cm=0.051m`

Peak emf of the first generator
`e_1=1.8Volt`

Peak emf of the second generator
`e_2=3.9Volt`

We know that induced emf is rate of change of magnetic flux , that is equal to magnetic field multiply by change in area

So emf will be proportional to the change in area

So
`(e_1)/(e_2)=(A_1)/(A_2)`

`(1.8)/(3.9)=(0.051^2)/(r_2^2)`

`r_2=0.075m = 7.5cm`

So the radius of the second coil will be 7.5 cm