Using Maxwell's laws nd ~E (r) and ~B (r) within a solenoid of
radius r, lenght...
Using Maxwell's laws nd ~E (r) and ~B (r) within a solenoid of
radius r, lenght l and with N turns provided that the current owing
within the solenoid changes as i = I cos (wt).
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You make a solenoid with a radius of 5.0 cm radius using a
copper wire of the length of 200 m and diameter of 0.05 cm.
what will be the magnitude of the magnetic field strength
along the axis of it, if you run a current of 30.0 A through
it?
Now you hold a circular loop of a wire with the radius of 8
cm
and a resistance of 2 ohm around this solenoid and want to
induce...
A solenoid (coil) of radius R has 10 turns per centimeter. It is
10cm long, and the coiled wire carries a current I. In addition to
the coil of wire, a second wire runs right down the central axis of
the solenoid, carrying a current of 2I. (The solenoid wire doesn't
intersect this second wire, because the former wraps around the
latter, always a distance R away.) A) Find the magnitude of the
total magnetic field at a distance R/2...
An ideal solenoid, of radius R and n turns per unit length, has
a current flowing through it. The current, I, varies with time, t,
according to I = I0 + at where I0 and a are constants. A conducting
ring of radius, r, is placed inside the solenoid with its axis
coinciding with the axis of the solenoid. The ring has a resistance
per unit length of H (in units of Ω/m).
(a) Use Lenz’s law to determine the...
1. An infinitely long solenoid of radius R carries n turns per
unit length and current I and is oriented such that its axis is
along the z direction. What direction must a particle of charge q
be moving such that it feels zero force (a) inside the solenoid (b)
outside the solenoid
2. Find the maximum magnetic flux through a circular coil of
radius L such that L < R placed inside the solenoid of the
previous problem.
Determine the radius r of a sphere centered on the nucleus
within which the probability of finding the electron for the ground
state of hydrogen is 53 % .
Determine the radius r of a sphere centered on the nucleus
within which the probability of finding the electron for the ground
state of hydrogen is 95 % .
Determine the radius r of a sphere centered on the nucleus
within which the probability of finding the electron for the ground...
The strength of the magnetic field within a solenoid is B = 3.9
x 10-2 T (outside the solenoid B = 0). A smaller, single loop is
placed in the solenoid parallel to the plane of each loop in the
solenoid. The resistance of the solenoid is 5.4 Ω, the resistance
of the loop is 0.29 Ω, the diameter of the solenoid is 0.07 m, and
the diameter of the loop is 0.04 m. An emf of 12 V is...
V=[(a b), a,b E R+] with (a1 b1)+(a2 b2)=(a1a2
b1b2)and for c E R, c(a b)=(a^c b^c) is a vector space over R.
Define T:R^2 to V by T[a b]= (e^a e^b). prove T is a linear
transformation from R2 to V.
A sphere of radius R has a radius dependent charge density ρ = B
· r3 in terms of R and B.
Calculate the potential as a function of r from the center of
the sphere.
A solenoid has N=1000 turns, length l=20 cm, and radius r=1.0
cm. (a) What is its self-inductance? (b) You are ramping up the
current from 0 to 1.0 A in 1.0 s. How much voltage do you have to
apply? (c) Calculate the energy stored in the inductor when the
current is 1.0 A.
Work out the products of the matrices E, R, R^2,R^3, A, B, C,
D,
and verify that these products reproduce the multiplication table
for the
symmetries of the square, as expected. (Instead of computing all 64
products,
compute “sufficiently many” products, and show that your
computations
suffice to determine all other products.)