Response:
Clarification:
Refer to the diagram indicating the charges on the specified sphere (see attachment).
The electric field at the stated positions is
E(r) = 0 for r≤a. Equation 1
E(r) = kq/r² for a<r<b. Equation 2
E(r) = 0 for b<r<c. Equation 3
E(r) = kq/r² for r>c. Equation 4.
We understand that electric potential correlates with the electric field through
V = Ed
A. To compute the potential at the outer surface of the hollow sphere (r=c), we determine that the electric field there is
E = kQ / r²
Then,
V = Ed,
At d = r = c
Thus,
Vc = (kQ / c²) × c
Vc = kQ / c
As a result, the total charge Q consists of +q, -q, and +q
Hence, Q = q - q + q = q
V = kq / c
B. To calculate the potential at the inner surface of the hollow sphere (r=b), we have
V = kQ/r
V = kQ / b, noting that r = b
So, Q = q
V = kq / b
C. At r = a
Following from equation 1:
E(r) = 0 for r≤a. Equation 1
The electric field at the surface of the solid sphere is 0, E = 0N/C
Thus,
V = Ed = 0 V
Consequently, the electric potential at the solid sphere's surface is 0.
D. At r = 0
The electric potential can be determined by
V = kq / r
As r approaches 0,
V = kq / 0
V approaches infinity.
Answer:
Maximum emf = 5.32 V
Explanation:
Provided data includes:
Number of turns, N = 10
Radius of loop, r = 3 cm = 0.03 m
It made 60 revolutions each second
Magnetic field, B = 0.5 T
We are tasked to determine the maximum emf produced in the loop, which is founded on Faraday's law. The induced emf can be calculated by:
For the maximum emf,
Therefore,
Hence, the maximum emf generated in the loop is 5.32 V.
Response:
a) , b)
Clarification:
a) The absolute pressure at a depth of 27.5 meters is:
b) The force applied by the water is:
Response:
Explanation:
Let T denote the tension.
By employing Newton's second law to analyze the bucket's downward motion, we have:
mg - T = ma
A torque, TR, acts on the drum, inducing an angular acceleration α in it. If I refers to the moment of inertia of the drum, then:
TR = Iα
Rearranging gives: TR = Ia/R
This leads to T = Ia/R²
Substituting this expression for T back into the previous equation yields:
mg - T = ma
mg - Ia/R² = ma
Consequently, we find that mg = Ia/R² + ma
Therefore, a (I/R² + m) = mg
This results in: a = mg / (I/R² + m)
Next, we aim to express T as:
mg - T = ma
which simplifies to mg - ma = T
Rearranging gives mg - m²g / (I/R² + m) = T
Thus, we arrive at: mg - mg / (1 + I / m R²) = T
For part (b), T = Ia/R²
and for part (c), the moment of inertia of a hollow cylinder calculates to:
I = 1/2 M (R² - (R² / 4))
This simplifies to 3/4 x 1/2 MR², yielding 3/8 MR²
Thus, I / R² = 3/8 M
When we substitute, we find a = mg / (3/8 M + m)
and subsequently T = Ia/R²
= 3/8 MR² × mg / (3/8 M + m) × 1/R²
Results in: