(a)(i) State Coulomb's law of electrostatics.
(ii) The electron and proton of a hydrogen atom are separated by a mean distance of \(5.2 \times 10^{-11}\,\text{m}\).
Calculate the magnitude of the electrostatic force between the particles.
[\(e = 1.6 \times 10^{-19}\,\text{C}\), \((4\pi \mathcal{E}_0)^{-1} = 9.0 \times 10^9\,\text{mF}^{-1}\)]
(b) The diagram below shows a potential divider circuit.
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i. Show that \(V_{\text{out}} = V_{\text{in}}\left(\frac{R_1}{R_1 + R_2}\right)\)
ii. If \(\frac{V_{\text{in}}}{V_{\text{out}}} = 2.5\) and \(R_2 = 30\,\Omega\), calculate \(R_1\)
iii. Define the volt.
(c) Explain why wood is not suitable for use as the core of transformers.
(d) State one application for the cathode ray tube.
(a)(i) Coulomb's law of electrostatics states that the force of attraction or repulsion between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, F = kQ1Q2/r^2, where F is the electrostatic force, Q1 and Q2 are the charges on the objects, r is the distance between them, and k is Coulomb's constant.
(ii) Using Coulomb's law, the magnitude of the electrostatic force between the electron and proton of a hydrogen atom can be calculated as follows:
F = k(Q1Q2/r^2) = (9.0 x 10^9 Nm^2/C^2)(1.6 x 10^-19 C)(1.6 x 10^-19 C)/(5.2 x 10^-11 m)^2 = 8.2 x 10^-8 N.
(b)(I) Proof of Vout
Let the current through the circuit be I
Vin
= I(R
1 + R
2
)
OR
I = VinR1+R2
V
out =
IR2
II. Calculation of R1
;
Vout
= V
in(
R1R1+R2
)
OR
VoutVin=R1R1+R2
12.5=R1R1+R30R
1 = 20
Ω
(ii) The Volt The unit of potential difference between two points when one joule of work is done in taking one coulomb of charge between the points
(c) Wood is not suitable for use as the core of transformers because it is not a good conductor of electricity. Transformers require a material with a high magnetic permeability, which allows for efficient transfer of energy between coils. Wood does not have the necessary magnetic properties and can also be damaged by the heat generated during operation.
(d) One application for the cathode ray tube (CRT) is in television and computer displays. A CRT works by producing a beam of electrons that is directed towards a phosphorescent screen, causing it to emit light and create an image. By controlling the path of the electron beam, the image can be manipulated and displayed on the screen. Although CRT technology has largely been replaced by LCD and LED displays, it is still used in some specialized applications such as medical imaging and oscilloscopes.
(a)(i) Coulomb's law of electrostatics states that the force of attraction or repulsion between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, F = kQ1Q2/r^2, where F is the electrostatic force, Q1 and Q2 are the charges on the objects, r is the distance between them, and k is Coulomb's constant.
(ii) Using Coulomb's law, the magnitude of the electrostatic force between the electron and proton of a hydrogen atom can be calculated as follows:
F = k(Q1Q2/r^2) = (9.0 x 10^9 Nm^2/C^2)(1.6 x 10^-19 C)(1.6 x 10^-19 C)/(5.2 x 10^-11 m)^2 = 8.2 x 10^-8 N.
(b)(I) Proof of Vout
Let the current through the circuit be I
Vin
= I(R
1 + R
2
)
OR
I = VinR1+R2
V
out =
IR2
II. Calculation of R1
;
Vout
= V
in(
R1R1+R2
)
OR
VoutVin=R1R1+R2
12.5=R1R1+R30R
1 = 20
Ω
(ii) The Volt The unit of potential difference between two points when one joule of work is done in taking one coulomb of charge between the points
(c) Wood is not suitable for use as the core of transformers because it is not a good conductor of electricity. Transformers require a material with a high magnetic permeability, which allows for efficient transfer of energy between coils. Wood does not have the necessary magnetic properties and can also be damaged by the heat generated during operation.
(d) One application for the cathode ray tube (CRT) is in television and computer displays. A CRT works by producing a beam of electrons that is directed towards a phosphorescent screen, causing it to emit light and create an image. By controlling the path of the electron beam, the image can be manipulated and displayed on the screen. Although CRT technology has largely been replaced by LCD and LED displays, it is still used in some specialized applications such as medical imaging and oscilloscopes.
