What is the magnitude of the charge inside the box?

[azazelis]

hey i have 2 problems I'm stuck on for my physics class. any help would be great.


1.

Let us assume that the Cassini-Huygens probe which landed on the Saturn's moon Titan on January 14, 2005 reported that it found a cubical box with a side of l=3.81 cm. Scientists in the flight center suspect that there may be electric charge inside the box and order the probe to measure the component of the electric field perpendicular to each side of the box before an attempt to open the box. The probe reports back that for four sides of the box the perpendicular component of the electric field is below the sensitivity of instruments and can be safely assumed to be zero, however, on the two opposite sides the probe measures a nearly uniform, inward-oriented, perpendicular component of the field with the magnitude of 22.7 N/C. It is your job to calculate the charge inside the box. You know that if the charge inside is negative and larger than 0.64 pC the discharge will most likely destroy the communication module of the probe and years of work and efforts may be lost. On the other hand, the box may contain the unprecedented information regarding inteligent life in our solar system.

What is the magnitude of the charge inside the box?

What i have: (22.7)*(8.85^-12)*(.0381^2)^2


2.

Suppose a large charged conducting plate with a surface charge density σ = +4.43 μC/m2 is located 5.0 cm from a drop of water. Suppose we consider a molecule of water for which the 2 H atoms (orange) and the O atom (blue) are co-planar with the electric field, and the angle θ between the direction of the point charges and one of the H atoms is 35.0 degrees, as shown. What is the magnitude of the torque on the water molecule?

What i have: ( σ / ε ) * (6.2E-30) * (sin 105/2+θ)


I have tried these about a hundred times and still can't get the answers. Any help would be amazing.

 

[StatusX]

1.

Let us assume that the Cassini-Huygens probe which landed on the Saturn's moon Titan on January 14, 2005 reported that it found a cubical box with a side of l=3.81 cm. Scientists in the flight center suspect that there may be electric charge inside the box and order the probe to measure the component of the electric field perpendicular to each side of the box before an attempt to open the box. The probe reports back that for four sides of the box the perpendicular component of the electric field is below the sensitivity of instruments and can be safely assumed to be zero, however, on the two opposite sides the probe measures a nearly uniform, inward-oriented, perpendicular component of the field with the magnitude of 22.7 N/C. It is your job to calculate the charge inside the box. You know that if the charge inside is negative and larger than 0.64 pC the discharge will most likely destroy the communication module of the probe and years of work and efforts may be lost. On the other hand, the box may contain the unprecedented information regarding inteligent life in our solar system.

What is the magnitude of the charge inside the box?

What i have: (22.7)*(8.85^-12)*(.0381^2)^2

I think that last square should be replaced by a factor of two, but besides that it looks ok.

2.

Suppose a large charged conducting plate with a surface charge density σ = +4.43 μC/m2 is located 5.0 cm from a drop of water. Suppose we consider a molecule of water for which the 2 H atoms (orange) and the O atom (blue) are co-planar with the electric field, and the angle θ between the direction of the point charges and one of the H atoms is 35.0 degrees, as shown. What is the magnitude of the torque on the water molecule?

What i have: ( σ / ε ) * (6.2E-30) * (sin 105/2+θ)

I don't think you've given enough information here. I'm sure the model of the water molecule you're given is greatly simplified, so you'll have to describe it more carefully.

 

[wais]

1. To calculate the charge inside the box, we can use the formula for electric field: E = kq/r^2, where E is the electric field, k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge.

Since we know the electric field (22.7 N/C) and the distance (l/2 = 1.905 cm) for one of the sides, we can rearrange the formula to solve for q:

q = Er^2/k = (22.7 N/C) * (0.01905 m)^2 / (8.99 x 10^9 Nm^2/C^2) = 9.59 x 10^-9 C

Therefore, the magnitude of the charge inside the box is 9.59 nanocoulombs.

2. To calculate the torque on the water molecule, we can use the formula for torque: τ = rFsinθ, where τ is the torque, r is the distance from the axis of rotation (in this case, the distance between the H atom and the O atom), F is the force, and θ is the angle between the force and the lever arm.

In this case, the force is the electric field acting on the molecule, and the lever arm is the distance between the molecule and the conducting plate (5.0 cm). So we can rewrite the formula as:

τ = (5.0 cm) * (Fsinθ) = (5.0 cm) * (σ/ε) * (sinθ) = (5.0 cm) * (4.43 x 10^-6 C/m^2) * (sin35.0°) = 1.06 x 10^-9 Nm

Therefore, the magnitude of the torque on the water molecule is 1.06 nanonewton meters.