Answer:
(a) A = m/s^3, B = m/s.
(b) dx/dt = m/s.
Explanation:
(a)
Therefore, the dimension of A is m/s^3, and of B is m/s in order to satisfy the above equation.
(b)
This makes sense, because the position function has a unit of 'm'. The derivative of the position function is velocity, and its unit is m/s.
Answer:
(a): The magnitude of the electric force on the small sphere =
(b): Shown below.
Explanation:
<u>Given:</u>
When the dimensions of the sheet is much larger than the distance between the charge and the sheet, then, according to Gauss' law of electrostatics, the electric field experienced by the particle due to the sheet is given as:
<em>where,</em>
is the electrical permittivity of the free space.
The electric field at a point is defined as the amount of electric force experienced by a unit positive test charge, placed at that point. The magnitude electric field at a point and the magnitude of the electric force on a charge q placed at that point are related as:
Thus, the magnitude of the electric force on the small sphere is given by
The sheet and the small sphere both are positively charged, therefore, the electric force between these two is repulsive, which means, the direction of the electric force on the sphere is away from the sheet along the line which is perepndicular to the sheet and joining the sphere.
<h2>(b):</h2>
When the sphere is in equilibrium, the tension in the fiber is given by the resultant of the weight of the sphere and the electric force experienced by it as shown in the figure attached below.
According to the fig.,
<em>where,</em>
<em />
g is the acceleration due to gravity.
