Answer:
a) V = k 2π σ (√(b² + x²) - √ (a² + x²))
,
b) E = - k 2π σ x (1 /√(b² + x²) - 1 /√(a² + x²))
Explanation:
a) The expression for the electric potential is
V = k ∫ dq / r
For this case, consider the disk formed by a series of concentric rings of radius r and width dr, the distance of each ring to point P
R = √(x² + r²)
The charge on a ring is
σ = dq / dA
The area of a ring is
A = π r
dA = 2π r dr
So the charge is
dq = σ 2π r dr
We substitute
V = k σ 2pi ∫ r dr / √(r² + x²)
We integrate
V = k 2π σ √(r² + x²)
We evaluate from the lower limit r = a to the upper limit r = b
V = k 2π σ (√(b² + x²) - √ (a² + x²))
b) the electric field and the potential are related
E = - dV / dx
E = - k 2π σ (1/2 2x /√(b² + x²) - ½ 2x /√(a² + x²))
E = - k 2π σ x (1 /√(b² + x²) - 1 /√(a² + x²))
The Volume of a Cube with a side(s) of 11.4 cm is
<span>V = s^3 </span>
<span> V = (11.4)^3 cm^3 </span>
<span> V = 1481.544 cm^3 </span>
<span> V = 1482 cm^3</span>
<span>however the Surface Area of a cube is the combined area of all the sides </span>
<span> A = 6s^2 </span>
<span> A = 6(11.4)^2 cm^2 </span>
<span> A = 779.76 cm^2 </span>
Answer:
Constructive interference
Explanation:
Here, the medium is same, same wavelength, same frequency, same amplitude and same direction of propagation.
Let the intensity of waves be I which is same for both
The formula for the net intensity is
where, Ф be the phase difference
So, 
Here, IR is maximum so the interference is constructive in nature.
Answer:
The correct option is (b).
Explanation:
We need to find the work done to increase the speed of a 1 kg toy car by 5 m/s.
We know that, the work done is equal to the kinetic energy of an object i.e.
So, 12.5 J of work is done to increase the speed of a 1.0 kg toy car by 5.0 m/s.
A scientist would write that number as 1.49 x 10⁸ kilometers .
(Or, if the scientist is in France or the UK, he might write it as 1.49 x 10⁸ kilometres .)
