Answer:
<h3>(A) The width

m</h3><h3>(B) The new width is

m</h3>
Explanation:
Given :
Focal length 
Maximum aperture
Wavelength
m
(A)
From rayleigh criterion,


rad
From angle formula,

Where
12 m ( given in example )
m

m
(B)
We know that
is proportional to the
and inversely proportional to the 
so we write the new width, here
is 5.5 times larger than above case

m
Let l = Q/L = linear charge density. The semi-circle has a length L which is half the circumference of the circle. So w can relate the radius of the circle to L by
<span>C = 2L = 2*pi*R ---> R = L/pi </span>
<span>Now define the center of the semi-circle as the origin of coordinates and define a as the angle between R and the x-axis. </span>
<span>we can define a small charge dq as </span>
<span>dq = l*ds = l*R*da </span>
<span>So the electric field can be written as: </span>
<span>dE =kdq*(cos(a)/R^2 I_hat + sin(a)/R^2 j_hat) </span>
<span>dE = k*I*R*da*(cos(a)/R^2 I_hat + sin(a)/R^2 j_hat) </span>
<span>E = k*I*(sin(a)/R I_hat - cos(a)/R^2 j_hat) </span>
<span>E = pi*k*Q/L(sin(a)/L I_hat - cos(a)/L j_hat)</span>
Momentum should be conserved. The momentum of both
objects must balance with their initial and final momentum.
Let m1 and v1 be the mass and velocity of the
bowling ball
And m2 and v2 be the mass and velocity of the
bowling pin
(m1v1)i + (m2v2)i = (m1v1)f + (m2v2)f
30 kg m/s + (1.5 kg)(0 m/s) = 13kg m/s + 1.5v2f
V2f = 11.33 m/s
<span>So the momentum = 1.5 kg(11.33 m/s) = 17 kg m/s</span>
Answer:

and

Explanation:
Given:
- first charge,

- second charge,

- position of first charge,

- position of second charge,

Now since there are only 2 charges and of the same sign so they repel each other. This repulsion will be zero at some point on the line joining the charges.
<u>Now, according to the condition, electric field will be zero where the effects of field due to both the charges is equal.</u>

- since first charge is greater than the second charge so we may get a point to the right of the second charge and the distance between the two charges is 1 meter.





Since we have assumed that the we may get a point to the right of second charge so we calculate with respect to the origin.

and
