# test 3-4 ```Test 3 Variant 4
Group
Name (TYPE)
NO communications
NO phones and any devices
1) A point charge q = -5 μC is surrounded by a
7) Find the power of energy dissipation P in the
sphere with radius r = 1 m.
resistor R = 100 Ω, if current I = 5 mA.
Find the electric flux Ф through the sphere.
Coulomb’s constant is k = 9&times;109 N&middot;m2&middot;C-2
Ans.:
2) Find the equivalent capacitance,
when the three capacitors С1 = 8 nF, С2 = 20 nF,
and С3 = 40 nF are connected in series.
Ans.:
8) The proton (q = +1.6&times;10-19 C) has velocity
υ = 2105 m/s.
The uniform magnetic field with magnitude B = 5 T
has angle with velocity direction α = 180&deg;.
Find Lorentz force F.
Ans.:
3) Find the electric potential energy U for a charge
q = +4 mC at the distance r = 9 cm from charge
Q = +40 C.
Ans.:
9) Two straight, parallel, superconducting cables
4.5 mm apart carry equal currents of
I = 1.5&times;10-3 kA.
Length of cables is l = 1 m.
Find force F of interaction between these cables.
μ0 = 4π&times;10-7 TmA-1
Coulomb’s constant is k = 9&times;109 N&middot;m2&middot;C-2
Ans.:
4) A wire has a diameter of d = 100 mm, the length
l = 314 m, and the resistivity ρ = 2&times;10-8 Ωm.
Find the resistance R.
Ans.:
10) The solenoid consists of a helical winding of
wire on a cylinder, usually circular in cross section.
The solenoid has n = 107 turns of wire per meter of
length and carries a current I = 10 A.
Find the magnitude of magnetic field B at the center
of the solenoid’s length.
Ans.:
5) Find the equivalent resistance,
when the three resistors R1 = 8 kΩ, R2 = 20 kΩ, and
R3 = 40 kΩ are connected in parallel.
Ans.:
11) The speed of sound at 20 &deg;C is υ = 344 m/s.
The frequency is f = 86 Hz.
Find the wavelength λ.
Ans.:
6) Find the work of electrical forces A in uniform
electric field with magnitude E = 1 N/C at
displacement L = 1 km of charge q = +103 mC in
the direction of the field.
Ans.:
12) Find the underdamped response of the oscillator
x at a moment in time t = 2 s if damping coefficient
is g = 4 s-1, the amplitude is A = 10 m, the period is
T = 1 s, the starting point (phase) is α = 0 on the
cosine fashion.
Ans.:
Ans.:
4
```