A thin condicting spherical shell of outer radius 20cm carries a charge of +3 muC. Sketch (a) magnitude of the electric field E and
(b) potential V versus the distance r from the center of the shell.
To sketch the magnitude of the electric field E and potential V versus the distance r from the center of the conducting spherical shell, we can use the following steps:
(a) Sketching the magnitude of the electric field E:
Step 1: Understand the properties of a conducting spherical shell carrying charge. In this case, the conducting shell has a positive charge, so the electric field lines will point radially outward.
Step 2: Determine the behavior of the electric field inside the shell. Due to the axial symmetry, the electric field inside a conducting shell is zero. Therefore, there will be no electric field lines inside the shell (E = 0).
Step 3: Determine the behavior of the electric field outside the shell. The magnitude of the electric field outside the shell can be given by Coulomb's law. The electric field (E) is directly proportional to the charge (Q) and inversely proportional to the distance squared (r^2) from the center of the shell.
E = k * Q / r^2
Step 4: Consider the charge distribution on the shell. Since the shell has a uniform charge distribution, the electric field magnitude will be the same at any point on the surface of the shell.
Step 5: Sketch the magnitude of the electric field E as a function of the distance r from the center of the shell. The electric field lines will start from the surface of the shell (since the electric field inside the shell is zero) and will diverge radially outward due to the inverse square dependence on the distance from the center.
(b) Sketching the potential V:
Step 1: Understand the properties of electric potential. Electric potential (V) is a scalar quantity that measures the work done to move a unit positive charge from infinity to a given point in an electric field. It determines the potential energy of a charge at that particular point.
Step 2: Determine the behavior of the potential inside and outside the shell. Inside the shell, the potential is constant since the electric field is zero. Outside the shell, the potential will change with the inverse of the distance from the center (V ∝ 1/r), similar to the electric field.
Step 3: Consider the reference point for potential measurements. To sketch the potential curve, a reference point at infinity can be chosen, where the potential is considered zero.
Step 4: Sketch the potential V as a function of the distance r from the center of the shell. The potential inside the shell will be constant (V = 0), while outside the shell, it will decrease as the distance r from the shell's center increases.
Note: The exact shape of the curves will depend on the specific values of charge and distance.