Find angle with pith ball and vertical wall

[britt]

1. The Question:
A 10.0 g pith ball, carrying a charge of 1.52 μC hangs from a thread attached to a charged vertical wall carrying a surface charge density σ = 3.57 μC/m2. Find the angle that the thread makes with the vertical.

Homework Equations

3. My attempt:

Tcosθ=mg Tsinθ=F
Canceling tension (sinθ/cosθ)=tanθ=(F/mg)
F=mgtanθ
σ=2ε₀E
E=σ/2ε₀=201694.9153
F=EQ=(201694.9153)(1.52E-6)=0.3065762712

F/mg= 0.0031283293 = tanθ
tan^-1(0.0031283293) = 0.17924

Is this the correct angle?

 

[gneill]

1. The Question:
A 10.0 g pith ball, carrying a charge of 1.52 μC hangs from a thread attached to a charged vertical wall carrying a surface charge density σ = 3.57 μC/m2. Find the angle that the thread makes with the vertical.

Homework Equations

3. My attempt:

Tcosθ=mg Tsinθ=F
Canceling tension (sinθ/cosθ)=tanθ=(F/mg)
F=mgtanθ
σ=2ε₀E
E=σ/2ε₀=201694.9153
F=EQ=(201694.9153)(1.52E-6)=0.3065762712

F/mg= 0.0031283293 = tanθ
tan^-1(0.0031283293) = 0.17924

Is this the correct angle?

Check your calculation of F/mg. The resulting value looks too small. Did you perhaps forget to change grams into kg for the mass?

 

[lightgrav]

what are you using for Fgrav? (check the mass units!)

 

[britt]

when i changed g to kg i got the angle to be 72.3

 

[gneill]

when i changed g to kg i got the angle to be 72.3

Yup. That looks better