Answer:
Electric field at (x, y, z): 
Explanation:
(a) The slab is of an insulating material and has a uniform charge distribution. We can visualize this as infinite number of point charges, distributed throughout the slab, equally spaced apart. So if we (hypothetically) start to calculate the electric field due to each charge at x = 0, we shall always find a charge at a mirrored position about the x = 0 plane (within x = -d and x = d) and hence will cancel out the electric field.
A simpler example would be an infinitely long wire of uniform charge distribution. Any point on the wire will have zero electric field has there are essentially equal number of charges on either side (the length of the wire being infinitely long)
(b) Let us take a cylinder as a Gaussian surface with base area A. We shall take advantage of the symmetry about x = 0 and shall position the cylinder perpendicular to the y-z plane with x = 0 being the mid-point. Now the electric flux will only flow out through the 2 bases of the cylinder. This is because the slab has infinite dimensions along y and z-axes (think of an infinite <em>sheet </em>of charge) and the electric field always starts out perpendicular to any surface of charges. If the Electric field at some point on the base of the cylinder be E, then total outgoing flux = 2EA
is the charge density, hence, 
where
is the length of the cylinder and
is the x-coordinate.
Therefore, using Gauss's law,

or, 
or, 
where,
= permittivity of free space.
Answer:
b
Explanation:
there is no net force on the basketball
Answer:
self-inductance is 23.4 mH
0.145 seconds it be turned off
Explanation:
given data
length L = 42.2 cm
diameter d = 10 cm
no of loop N = 1000 loops
induced emf = 3 V
current I = 18.6 A
to find out
self-inductance and How fast it turned off emf
solution
we apply here formula of self-inductance that is
self-inductance = u×N²×A / L .......................1
put here value
self-inductance = 4π×1000²×(π×r² / 0.422)
self-inductance = 4π×1000²×(π×0.05² / 0.422)
self-inductance = 0.0234 H
so self-inductance is 23.4 mH
and
we know emf = Ldi /dt
so time = 0.0234 × 18.6
time = 0.145 seconds
Answer:
a)Vr= 5 mph
b)Vr= 115 mph
Explanation:
Lets
your velocity ,u= 60 mph
velocity of truck ,v= 55 mph
When object are moving in opposite direction the relative velocity = u +v When object are moving in opposite direction the relative velocity = u - v
a)
Truck is moving in the same direction ,so the relative velocity
Vr= = u - v
Vr= 60 - 55
Vr= 5 mph
b)
Truck is moving in the opposite direction ,so the relative velocity
Vr= = u+v
Vr= 60 + 55
Vr= 115 mph