Electricity is one of the fundamental aspects of life’s enjoyment. To be called a city, developing or developed country, there is a need for a constant power supply (electricity). Electricity goes hand in hand with magnetism. therefore to understand the basic principles of electricity and magnetism, the following must be analyzed.
- Charges
- Electrostatic
- Conductor and current
- Dielectric
- Magnetic field and induction
- Maxwells equations
- Electromagnetic equations and waves.
Etc
An electron is accelerated by a constant electric field of magnitude 300N/C. Find the acceleration of this electron.
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A sheet of aluminum foil of negligible thickness is introduced between the plates of capacitor. The capacitance of the capacitor will………
C = Eo a/d
As d decreases C increases
The difference in the potential between the accelerating plates of a TV set is about 25kV. If the distance between these plates is 1.5cm. Find the uniform electric field in this region.
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A piece of aluminum foil of mass 5×10-2kg is suspended by a string in an electric field directed vertically upward. If the charge on the foil is 3uC. Find the strength of the field that will reduce the tension in the string to zero
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Two point charges +8q and -2q are located at x = 0 and x = L respectively. The location of a point on the x – axis at which the net electric field due to these two point charges is zero is
ƩE = E1 + E2 = 0
Kq1 / r2 + Kq2 / r2 = 0
8Kq / x2 – 2Kq / (L – X)2 = 0
8Kq / x2 = 2Kq / (L – X)2
8Kq / 2Kq = x / (L – X)2
4 = x / (L – X)2
4(L – X)2 = x2
4 (L2 – 2LX + X2) = X2
4L2 – 8LX + 4X2 = X2
4L2 – 8LX + 3X2 = 0
4 X 3 = 12 – 6 – 2 = – 8
4L2 – 6LX – 2LX + 3X2 = 0
2L (2L – 3X) – X (2L – 3X) = 0
(2L – 3X) (2L – X) = 0
2L – 3X = 0 OR 2L = X
2L = 3X
X = (2/3) L or x = 2 L
A point Charge of 2uC is at the center of a cubic Gaussian surface 9cm on edge. What is the net electric flux through the surface?
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In the Bohr Theory of hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is 0.53 x 10-10m. Find the electrostatic force acting on each particle.
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An electron starts from rest 3cm from the center of a uniformly charges insulating sphere of radius 2cm and total charge of 1nC. What is the speed of the electron when it reaches the surface of the sphere?
The electric field 2m from a point charge has a magnitude of 8 x 104 NC-1. What is the strength of the electric field at a distance of 4m?
. F = 0.8 N q1 = q2 = q r = 0.1m
F = K q1 q2 / r2 0.8 = k q2 / 0.12
0.8 × 0.12 = 9.0 × 109 x q2
q2 = 0.8 × 0.12 / 9.0 x 109
q = 9.4 × 10-7 C
The capacitance of a capacitor can be increased or decreased by
sliding the plates
The distance between two charges q1 = +2mC and q2 = +6mC is 15cm. calculate the distance from charge q1 to the points on the line segment joining the two charges where the electric field is zero
q1 = +2µC q2 = + 6 µC r = 15cm = 0.15m
E1 + E2 = 0
K×2µ / x2 + K×6µ / (x – 0.15)2
2µk / x2 = 6µk / (x – 0.15)2
6/2 = (x – 0.15) /x2
3x2 = (x – 0.15)2
3x2 = x2 – 0.3x + 0.152
2x2 + 0.3x – 0.152
X = 0.055m or – 0.2 m X=5.5cm
An electron is positioned in an electric field. The force on the electron due to the electric field is equal to the force of gravity on the electron. What is the magnitude of this electric field?
Fe=Fg
Fe = Eq
Fg = mg
Hence Eq = mg
E=mg/q
E= 9.11×10-11 x 9.81 / 1.6 x 10-19 = 5.58×10-11 N/C
The electric flux through a surface will be minimum, when the angle between E and A is?
Ф= EA cos φ
When φ = 90o
φ = 0 (minimum)
The electric field 2m from a point charge has a magnitude of 8 x 104 NC-1. What is the strength of the electric field at a distance of 4m?
E = 8 x 104 N/C
E = Kq/r2 8 x 104 = (9x 109 x q)/ 22
q = (22 x 8×104)/ 9 x 109 = 3.55 x 10-5 C
E2 = kq / r2 = 9 x 109 x 3.55×10-5 / 42
= 2.0 x104
A negative charge in an electric field experiences a force accelerating it due south. What is the direction of the electric field?
negative chargers accelerate in a direction opposite to the direction of the field
A circular plane, with a radius of 2.2m, is immersed in an electric field with a magnitude of 800N/C. The field makes an angle of 200 with the plane. What is the magnitude of the electric flux through the plane?
r = 2.2m
E = 800 N/c
φ = 90o – 20o =70o
Flux =?
Ф = EA cos φ
A = πr2 = π x 2.22
Ф = 800 x π x 2.22 cos 70 = 4.2 x 103 Nm2/C
A glass rod rubbed with silk thread is a
positively charged
Consider two parallel plates capacitor separated 15cm apart, where the electric field between them is 100 V/m, and the charge on either plates is 30mC. What is the capacitance of the capacitor?
d = 1.5 cm
E = 100 V/m q = 30 µC
C = Q/V
where V = Ed
= 100 x 0.015 = 1.5 v
C = 30 x 10-6 / 1.5 = 20 mF
C = 2x 10-5 F
If an electric charge is moved from lower power potential to higher potential, then energy should be……..
Supplied
What is the electric potential energy of an electron located 5.3 x 10-11 m from the proton in hydrogen atom?
H atom d = 5.3 x 10-11 m
UE = Kq1q2 / r charge on electron is the same as proton
UE = 9 x 109 x – 1.6 x 10-19 x 1.6 x 10-19 / 5.3 x 10-11
= – 4.347x 10-18g
A particle with a charge of 2.4 x 10-5C is accelerated from rest through a potential difference of 6.2 x 104 V. if the final speed of this particle is 9.3 x 103ms-1, what is the mass of the particle
. q = 2.4 x 10-5C
V = 6.2 x 104 V
m =?
u = 0 m/s
Conservation of energy.
½ mv2 = qV
m = 2qV/v2 = 2 x 2.4 x 10-5 x 6.2×104 / (9.3 x 103)2 = 3.4 x 10-8
An electron experiences an electric force of 1.8 x 10-11N at a distance of 5 x 10-9m from the nucleus of an ion. The electron is moved farther away to a distance of 2 x 10-8m from the ion. What is the new electric force on the electron?
F1 = 1.8 X 10-11 N
r1 = 5 x10-9m
r2 = 2×10-8
F2 =?
At r1 = force = F1
At r2 force = F2
F = Kq1q2 = K q1q2 = constant
F α 1/r2 F = c/r2 c = constant
Fr2 = C
F1r21 = F2r22
F2 = F1r21 / r22 = 1.8×10-11 x (5×10-9)2 /(2×10-8)2
=1.125×10-12N
Due to a large quantity of electric charge which builds up in the heavy thunderclouds, the phenomenon occurs is called………
Snow
Calculate the total capacitance if C1 = C2 = C3 = 3mF
. C1 = C2 = C3 = 3µF
Total C = C1 // C2 + C3
= 3 x 6 / 3 + 6 = 18/9 = 2µF
If ta velocity Vab = 6V is applied, what is the change on C3?
Q = CV
QT = 2 × 6 = 12 C
Vab = 6V
QT = Q1 = Q2 = Q3 ………….
Q parallel = 12 µC
V3µf = 2µf / 3µf x 6v = 4v
V6µf = (2µF/6µf) x 6 = 2v
We have
Q = CV
QC3 = 3 × 2 = 6 C
A capacitor has a charge of 3mC When the voltage across the capacitor is 12V. what is the energy stored in the capacitor?
Q = 3nC
V = 12 V
U = ½ CV2
Q = CV = C = u/v
U = ½ QV = ½ x 3 x 10-9 x 12 = 1.8 x 10-8J
Two parallel plates separated by distance of 1cm have a potential difference of 20V between them. The plates are held in horizontal position with the negative plate above the positive plate. An electron is related from rest in the upper plate. What is the magnitude of the magnitude of the acceleration of the electron?
d = 1 cm V = 20v
= 0.01m
Thunderclouds are charged by friction between
water molecules and air
When a charge is accelerated trough a potential differences of 500V, its kinetic energy increases from 2 x 10-5 j to 6 x 10-5 j. what is the magnitude of the charge?
V = 500V
Δu = 2 x 10-5 – 6 x 10-5
Q =? = – 4 x 10-5 J
Δu = QV
Q = Δu / V = – 4 x 10-5 / 500 = – 8 x 10-8 C = 8 X 10-8 C (magnitude)
To distinguish between insulators and conductors, we can use ………
Electroscope
Consider a capacitor made of two 0.05mm, if the capacitance is 3nF, what is the relative permeability, kg of the material between the plates?
. A = 0.05m2 d = 0.5 mm C = 3 nF µr =?
C = Ɛ.A/ d
Ɛ = C x d / A = 3 x 10-9 x 0.5 x 103 / 0.05 = 3 x 10-11
Ɛ = ƐoƐr Ɛr = Ɛ/Ɛo = 3 x 10-11/ 8.85 x 10-12 = 3.39
On a dry day if we walk in a carpet room and then touch some conductor we will fell
8 (Electrostatics)
Two electrons are held 3mm apart when released from a rest, what is the velocity of each electron when they are sum apart?
r = 3µm r2 = 8µm
Change in electrostatic energy = Δ in KE
Kq2/ r2 – Kq2/ r1 = ½ MV2 X 2
Kq2(1/r2 – 1/r1) = Mv2 s
9 x 109 x (- 1.6 x 10-19)2 (1/8 x 10-6 – 1/3 x 10-6) = 9.11 x 10-31 x v2
The lines of electric field were introduced by …………
Michael faraday
What distance must separate two charges of +5.6 x 10-4C and – 6.3 x 10-4C in order to have an electric potential energy with magnitude of 5j in the system of the two chares?
q1 = 5.6 x 10-4 C q2 = – 6.3 x 10-4
U= 5j U = kq1q2/ r
r = kq1q2/U
r = 9x 109 x 5.6 x 10-4 x 6.3 x 10-4 / 5
= 6.35m
2 x 107 electrons pass through a conductor in 1 x 106 sec. the current flowing will be……..
. n = 2 x 107 electrons, t = 1 x 10-6s
Q = It
Total charges carried by n electrons is
Q = n x e = 2 x 107 x 1.6 x 1011 C
I = Q/t = 2 x 107 x 1.6 x 1011 / 1 x 10-6 = 3.2 x 10-6 A
Potential difference of a battery is 2.2V when it is connected across a resistance of 5Ω. If suddenly the potential difference falls to 1.8V, its internal resistance will be will be………..
Rheostat can also be used as a ……..
variable resistor & potential divider
Reciprocal of resistance is called
Conductance
The heating effect of electric current is used in?
electric kettle
The potential difference needed to stop an electron having an initial speed of 4.2 x 105 m/s is
qV = ½ mv2
V = 4.2 x 105m/s
q = e = 1.6 x 10-19C m = 9.11 x 10-31kg
= 1.6 x 10-19 x V = ½ x 9.11 x 10-3 x (4.2 x 105)2
V = 1V
What resistance should you place in parallel with a 560 Ω resistor to get an equivalent resistance of 45KΩ?
R1 = 56KΩ R2 =?
RT = 48 KΩ
For the two resistor in //
RT = R1R2 / R1 + R2
45 = 56 × R2 / 56 + R2
45 (56 + R2) = 56 R2
2520 + 45R2 = 56R
11R2 = 2520
R2 = 229KΩ
To determine the resistance of a resistor one has to measure the across the terminals of resistor and divide it flowing through the resistor.
voltage, current
Storing electricity is achievable using……..
A capacitor
The resistance of a 120V light bulb that drawn a current of 1.25A is
R = V/I
= 120/1.25
= 96 Ω
A resistor R and another resistor 2R are connected in series across a battery. If heat is produced at a rate of 10W in R, then in 2R it is produced at rate of
P = I2R
Same current passes through R and 2R hence can be taken as constant
If PR = 10 MW
Then P2R = 2 X PR = 20 MW
A cell of emf 12V and internal resistance of 20Ω is connected to an electric lamp of 100Ω. Calculate the current flowing through the circuit
V = 12v r = 20 Ω R = 100Ω
V = I (R + r)
I = 12/(20 + 100) = 12/120
= 1/10 = 0.1 A
Experimental evidence indicates that
charge is conserved but not quantized
Wire A, which is at the same length and material as wire B, has twice the diameter of wire (B) if the resistance of wire B is R, what is the resistance of wire A?
LA = LB
R = pl/A
PA = PB dA = 2dB
RB = R RA =?
RB = lB/AB = R where AB = πdB2 / 4
but dB= dA/2
AA= π(2dB)2/4) = 4πdB2/4)
AA= π(dB)2
Since AB = π(dB)2/4
AB = AA/4 or AA= 4AB
From (A) RB – ᴩl/AB = R RA = ᴩl/AB
RA = ᴩl RA x ¼ (R) = R/4
When a portable radio is playing, the current in the radio is 300mA. If the resistance of the radio is 30Ω, what is the voltage supplied by the radio battery?
I = 300 mA
R = 30Ω
V = IR = 300 x 10-3 x 30
= 9V
If a voltage of 2V exist across three capacitors with capacitance 1Mf, 2mf and 3mf connected in parallel, what is the total charge enclosed in the system?
CT = 1 + 2 + 3 = 6µF
V = 2V
Q = CV = 6 x 2 = 12 µF
Two 3mf parallel capacitors are connected to a 6mf capacitor in series, the equivalent capacitance is……………
C parallel = 3 + 3 = 6 µF
C total = 6 x 6 / 6 + 6 = 36/12 = 3µF
A toaster rated at 600W is connected to a 120V source. What current does the toaster draws from the source?
P = 600W V = 120V
P = IV
I = P / V = 600/120 = 5A
Three 2Ω series resistors are connected to a 6Ω resistor in parallel, the equivalent resistance is
RSeries = 2 + 2 + 2 = 6Ω
RTotal = 6//6 = 6 x 6 / 6 + 6 = 36/12 = 3Ω
A coil of wire has a resistance of 20Ω at 25oC and 25.7Ω at 100oC. calculate the temperature coefficient.
R1 = 20Ω T1 = 25OC
R2 = 25.7Ω T2 = 100OC
R2 = R1 (1 + α [T2 – T1])
25.7 = 20 [1 + α [100 – 25]
25.7/20 = [1 + 75α]
α = 3.8 X 10-3 OC
The current in the circuit is
RT = 10 + 8 = 18V
E = 6 – 12 = – 6
I = – 6 / 18 = -1/3
The current in the circuit if the 6V battery is reversed will be
V = E = 6 + 12 = 18v
R = 10 + 8 = 18v
I = V/R = 18 / 18 = 1A
Use the figure 3 above to find the total resistance of the circuit.
RT = 1Ω || 1 Ω + 1Ω ||1Ω
(1 x 1/ 1 + 1) + (1 x 1/ 1 + 1)
= ½ + ½ = 1Ω
The value of the current i2 in figure 4 above is
RT = 4 || 4 = 4 x 4 / 4 + 4 = 2
V = IR = 4 x 2 = 8v
V is same in parallel
I1 = 8/4 = 2A
Compute the equivalent resistance in the circuit in figure 5 above and find the current flowing.
RT = 4 + 6||3
6||3 = 6 × 3/ 6 + 3 = 18/9 = 2Ω
RT = 4 + 2 = 6Ω
I = V/R = 18/6 = 3A
A circular area with a radius of 6.5cm lies in the x-y plane, what is the magnitude of the magnetic flux through this circular due to a uniform magnetic field of 0.23T that points in the +z direction?
r = 6.5 cm
B = 0.23W/m2
Ф = BA
A = πr2 = π x 0.652 = 4.225 x 10-3 m2
Ф = BA
Ф = 9.71 x 10-4 Wb
Find the force acting on a conductor 3m long carrying a current of 50A at right angles to a magnetic field having a flux density of 0.67T
F =? = 3m I = 50A
B = 0.67 T
F = BIL = 0.67 X 50 X 3 = 100.5
A loop which is 6cm long and 2cm wide is placed in a magnetic field of 0.2T. the loop contains 200 turns and carries current of 50mA, the torque on it is?
A = 6cm × 2cm B = 0.02 T N = 200
I = 50mA
T = BANI = 0.02 x 0.06 x 0.02 x 200 x 50 x 10-3
T = 2.4 X 10-4 Nm
A certain current produces a magnetic field B near the center of a solenoid if the current is doubled, the field near the center will be………..
When a charged particle moves at right angle to a magnetic field the quantity that changes is………….
Momentum
Two point like objects with electric charges q1 = 0.5nC and q2 = -0.3nC are separated by a distance 0.4m. How much work is required to transport a third charge q3 = 0.2nC from infinitely far away to a position exactly at the midpoint of line connecting the two other charges?
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