sphere A has a mass of 4.2*10^-2 kg and is tethered to a wall by a thin thread. Sphere a has an excess of 1.2 *10^12 electrons. Sphere B has a deficit of 3.5*10^12 electrons and is o.23 m from sphere A
a) determine the angle between the thread and the wall
b) determine the tension in the thread
To determine the angle between the thread and the wall, we can use the concept of electric field lines. The electric field lines radiate outwards from the charged object.
a) Determine the angle between the thread and the wall:
First, we need to find the direction of the electric field between the two spheres. Since sphere A has an excess of electrons and sphere B has a deficit of electrons, the electric field between them will point from sphere A to sphere B. Therefore, the electric field lines will be directed from sphere A towards sphere B.
Now, we can consider the thread as being at equilibrium, meaning the net force acting on the thread must be zero. The force acting on the thread is the tension in the thread, and the direction of the electric field acts along the thread.
Since the thread is tethered to the wall, it must be perpendicular to the wall. Therefore, the angle between the thread and the wall will be 90 degrees.
b) Determine the tension in the thread:
To find the tension in the thread, we need to consider the net force acting on sphere A due to the electric field and the gravitational force.
The gravitational force acting on sphere A is given by F_grav = m * g, where m is the mass of sphere A (4.2 * 10^-2 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The electric force acting on sphere A is given by F_elec = q * E, where q is the excess charge on the sphere A (1.2 * 10^12 electrons) and E is the electric field due to sphere B at the location of sphere A. The electric field at a distance r from sphere B is given by E = k * (|Q| / r^2), where k is the Coulomb's constant (approximately 8.99 * 10^9 Nm^2/C^2), |Q| is the magnitude of the charge on sphere B (3.5 * 10^12 electrons converted to Coulombs), and r is the distance between the two spheres (0.23 m).
Once we have both the gravitational force and the electric force, we can find the tension in the thread by equating the net force to zero. The tension in the thread will be equal in magnitude but opposite in direction to the net force.
Therefore, solving the equation F_grav + F_elec = 0 will give us the tension in the thread.