Question

A spring with an unstrained length of 0.070 m and a spring constant of 1.9 N/m hangs vertically downward from the ceiling. A uniform electric field directed upward fills the region containing the spring. A sphere with a mass of 5.8 × 10-3 kg and a net charge of +7.2 μC is attached to the lower end of the spring. The spring is released slowly, until it reaches equilibrium. The equilibrium length of the spring is 0.062 m. What is the magnitude of the external electric field?

Answer 1

Electric field is equal to 15005.5 N/C

Step-by-step explanation:

We have given unstrained length of spring = 0.070 m

Spring constant = 1.9 N/m

Equilibrium length of spring = 0.062 m

Change in length of spring x = 0.070 - 0.062 = 0.008 m

Mass of sphere
`m=5.8* 10^[-3]kg`

Charge on sphere
`q=7.2* 10^[-6]C`

Spring force is equal to
`F=Kx=1.9* 0.008=0.0152N`

Mg force on the sphere
`mg =5.8* 10^(-3)*9.8=0.0568N`

Force on the sphere is equal to

`qE=mg+F_(spring)`

`7.2* 10^(-6)* E=0.0512+0.05684=0.1080`

`E=15005.5N/C`