Tension (related to Fe) Question and Gauss Question

[mudkip]

I have two questions

Regarding tension:
Two balls are suspended as a pendulum from a shared point. The balls are held at angle theta (due to electric force). I understand that I am supposed to add the forces of the tension, the electric force and the force due to gravity, and that they should total zero, but for some reason I'm having issues with solving for tension. Should I be finding x component and y component of T and find a resultant T to then add to Fg and Fe? Or should I add the x components of Fg and Fe and Ft and then the y components of the same and then find resultant force? I'm solving for T so I can find Fe, which I'll then use to find q. The mass of the balls are the same.

Regarding Gauss:
My textbook offers no insight into how to compute electrical fields for concentric shell and sphere, and I can't seem to find much through internet searches. Wondering if someone could help explain how to solve for such a thing.

 

[Office_Shredder]

For the tension... if you know the angle, you should also be able to calculate the vertical component (what's holding the balls up?). Then you can calculate the total tension.

If you don't know the angle, keep in mind that two forces are acting on the ball (that the tension is opposing): electric and gravitational. They should form a vector directly opposite the direction of the tension force

For Gauss:

Draw a sphere around your spherical charge. You know Integral(EdA)=q/e (e is epsilon). E is constant, and the surface area of a sphere is 4*pi*r^2

 

[kyle8921]

Regarding tension:

To solve for tension in this situation, you will need to use vector addition. This means finding the x and y components of each force (tension, electric force, and force due to gravity) and then adding them together to find the resultant force. You can then set the resultant force equal to zero, since the balls are in equilibrium, and solve for tension.

Alternatively, you could also solve for tension by using trigonometric functions. In this case, you would use the angle theta and the known magnitude of the forces to find the magnitude of tension.

Regarding Gauss:

To compute electrical fields for concentric shells and spheres, you can use Gauss' Law. This law states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. In simpler terms, this means that the electric field at a point outside a charged shell or sphere is the same as the electric field at a point inside that shell or sphere. You can use this law to solve for the electric field at any point outside or inside the shell or sphere.

To apply Gauss' Law, you will need to use the following equation: E = Q/4πεr^2. Here, E is the electric field, Q is the charge enclosed by the surface, ε is the permittivity of free space, and r is the distance from the center of the shell or sphere to the point where you want to find the electric field.

I hope this helps to clarify things for you. If you need further assistance, I suggest consulting with your teacher or a tutor for additional support. Good luck with your studies!