PRELIMINARY STAGE 2024
Contest 7
Tepa SHS: 40 points (Winner)
Bright SHS: 39 points
Sekondi College: 27 points
Contest 8
Queen of Peace SHS: 34 points (Winner)
Sonrise Christian High School: 31 points
Presby SHS, Bompata: 30 points
Contest 9
Navrongo SHS: 39 points (Winner)
St. Mary’s Seminary SHS, Lolobi: 36 points
Bolgatanga Girls’ SHS: 29 points
ROUND 3 - PROBLEM OF THE DAY
ROUND 3 PROBLEM OF THE DAY
Discuss magnetic flux and magnetic flux density with respect to:
- Type of quantity (vector or scalar)
- SI unit and symbol
- Physical relationship between them
- Relationship between their SI units
SOLUTION:
A.
Type of quantity:
- Magnetic Flux: Scalar quantity.
It represents the total amount of magnetic field passing through a given surface area, accounting only for magnitude.
- Magnetic Flux Density: Vector quantity.
It possesses both a specific magnitude (the strength of the magnetic field) and a distinct directional orientation in space.
B.
SI Unit and Symbol:
- Magnetic Flux: Weber, symbol Wb
- Magnetic Flux Density: Tesla, symbol T
C.
Physical relationship between them:
Magnetic Flux ($\Phi$) is the surface integral of the Magnetic Flux Density vector ($\mathbf{B}$) over an oriented area vector ($\mathbf{A}$).
For a uniform magnetic field passing through a flat surface, this physical link simplifies directly to a dot product:
$\Phi = \mathbf{B} \cdot \mathbf{A}$
$\Phi = B A \cos\theta$
where $\theta$ is the angle between the magnetic field vector and the normal vector (perpendicular line) of the surface area.
D.
Relationship between their SI units:
- 1 Tesla = 1 Weber per square meter ($1\text{ T} = 1\text{ Wb/m}^2$)
- 1 Weber = 1 Tesla meter squared ($1\text{ Wb} = 1\text{ T}\cdot\text{m}^2$)
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PRACTICE QUESTIONS
1. QUESTION: Distinguish between magnetic flux density (B) and magnetic field strength (H).
ANSWER: B is measured in teslas and includes the effect of the material; H is measured in A/m and depends only on the currents; $B = \mu H$.
SOLUTION:
Both are vectors.
2. QUESTION: Distinguish between EMF and potential difference.
ANSWER: Both are scalars in volts; EMF is energy supplied per unit charge by a source, PD is energy converted per unit charge between two points; $\varepsilon = V + Ir$.
SOLUTION:
The difference is the drop across the internal resistance.
3. QUESTION: Distinguish between electric field and electric flux.
ANSWER: Electric field is a vector in N/C; electric flux is a scalar in N m²/C; $\Phi = \mathbf{E}\cdot\mathbf{A}$.
SOLUTION:
Flux is the field through a surface.
4. QUESTION: Distinguish between charge and current.
ANSWER: Charge is a scalar in coulombs; current is a scalar in amperes, the rate of flow of charge; $I = \dfrac{Q}{t}$.
SOLUTION:
1 A = 1 C/s.
5. QUESTION: Distinguish between capacitance and charge.
ANSWER: Capacitance is in farads, the charge stored per volt; charge is in coulombs; $Q = CV$.
SOLUTION:
Both are scalars.
6. QUESTION: Distinguish between resistance and resistivity.
ANSWER: Resistance (Ω) belongs to a particular conductor; resistivity (Ω m) belongs to the material; $R = \dfrac{\rho L}{A}$.
SOLUTION:
Both are scalars.
7. QUESTION: Distinguish between self-inductance and mutual inductance.
ANSWER: Both are in henries; self-inductance links a coil's own changing current to its EMF, mutual inductance links one coil's current to another coil's EMF.
SOLUTION:
$\varepsilon = -L\dfrac{dI}{dt}$ and $\varepsilon_2 = -M\dfrac{dI_1}{dt}$.
8. QUESTION: Distinguish between magnetic flux and flux linkage.
ANSWER: Flux (Wb) is BA through one turn; flux linkage (Wb-turns) is NΦ for a coil of N turns.
SOLUTION:
Induced EMF equals the rate of change of flux linkage.
9. QUESTION: Distinguish between electric potential and electric potential energy.
ANSWER: Potential (V) is energy per unit charge; potential energy (J) is the energy of a particular charge; $U = qV$.
SOLUTION:
Both are scalars.