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The potential difference between the accelerating plates of a TV set is about \(25 \mathrm{kV}\). If the distance between the plates is \(1.5 \mathrm{~cm}\), find the magnitude of the uniform electric field in the region between the plates.

Short Answer

Expert verified
The magnitude of the uniform electric field in the region between the plates is \(1.67 x 10^6 V/m\).

Step by step solution

01

Conversion of units

First, convert the given measurements to SI units. The potential difference is given as \(25 kV\), since 1 kV = 1000 Volts, this is equivalent to \(25000 V\). Similarly, the distance is given as \(1.5 cm\), convert this to meters by dividing by 100, obtaining \(0.015 m\).
02

Computation of electric field

Now, substitute the SI unit values obtained from step 1 into the equation for electric field \(E = V/d\). This gives \(E = 25000 V / 0.015 m\).
03

Solution

By calculating the values, the magnitude of the electric field is found to be \(E = 1.67 x 10^6 V/m\). This is the final answer

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Potential Difference
Understanding the potential difference is key when learning about electric fields. It's often compared to the 'electrical pressure' that can push charges through a circuit or in our example, across TV set plates. The potential difference is measured in volts (V), and it's the energy difference that would be given to each charge moving between two points.

In the context of the TV set example, a potential difference of 25 kilovolts (kV) is quite high. It means that electrons being accelerated across the plates inside the TV are given a substantial amount of energy. Hence, they move rapidly from one plate to the other, which is essential for the TV's operation. This potential difference, once converted to standard international (SI) units as volts, becomes a foundational value for calculating the electric field's strength.
Electric Field Strength
The electric field strength is a measure of how strong the electric field generated between two points is. Essentially, it tells us how much force a charge would feel in that field. This strength is directly proportional to the potential difference and inversely proportional to the distance between the plates generating the field.

The equation to calculate this is quite straightforward:
\[ E = \frac{V}{d} \]
where E represents the electric field strength (in volts per meter, V/m), V is the potential difference (in volts, V), and d is the distance between the plates (in meters, m). Understanding this relationship is fundamental to physics problem solving, particularly in electromagnetism.
Unit Conversion

Importance of SI Units

Unit conversion is a crucial step in solving physics problems accurately. SI units, or the International System of Units, provide a standard that enables scientists and engineers worldwide to communicate their findings and calculations unambiguously.

For instance, converting kilovolts to volts, multiplying by 1,000, and centimeters to meters, dividing by 100, ensures that we apply the correct scale to the problem. Otherwise, miscalculations may occur, leading to incorrect results and interpretations. It's always important to remember to convert all your measurements to SI units before proceeding with any calculations.
Physics Problem Solving
Solving physics problems requires a methodical approach. In our example, we first convert all units to the SI standard, then we apply the relevant formulas to find the unknown quantity.

Understanding the concepts behind the formulas, such as potential difference and electric field strength, is just as important as the mathematical computation itself. This comprehensive understanding aids in not only deriving the correct solution but also in grasping the physical implications of the result.

Following a step-by-step method ensures that all aspects of the problem are considered and that calculations are carried out systematically. Finally, interpreting the results in the context of the real world, such as the operation of a TV set's internal mechanism, allows the theoretical physics to come to life.

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Most popular questions from this chapter

A parallel-plate capacitor with area \(0.200 \mathrm{~m}^{2}\) and plate separation of \(3.00 \mathrm{~mm}\) is connected to a \(6.00-\mathrm{V}\) battery. (a) What is the capacitance? (b) How much charge is stored on the plates? (c) What is the electric field between the plates? (d) Find the magnitude of the charge density on each plate. (e) Without disconnecting the battery, the plates are moved farther apart. Qualitatively, what happens to each of the previous answers?

(a) Find the potential difference \(\Delta V_{e}\) required to stop an electron (called a "stopping potential") moving with an initial speed of \(2.85 \times 10^{7} \mathrm{~m} / \mathrm{s}\). (b) Would a proton traveling at the same speed require a greater or lesser magnitude potential difference? Explain. (c) Find a symbolic expression for the ratio of the proton stopping potential and the electron stopping potential, \(\Delta V_{p} / \Delta V_{r}\) The answer should be in terms of the proton mass \(m_{p}\) and electron mass \(m_{r}\)

A certain storm cloud has a potential difference of \(1.00 \times 10^{8}\) V relative to a tree. If, during a lightning storm, \(50.0\) C of charge is transferred through this potential difference and \(1.00 \%\) of the energy is absorbed by the tree, how much water (sap in the tree) initially at \(30.0^{\circ} \mathrm{C}\) can be boiled away? Water has a specific heat of \(4186 \mathrm{~J} / \mathrm{kg}^{\circ} \mathrm{C}\), a boiling point of \(100^{\circ} \mathrm{C}\), and a heat of vaporization of \(2.26 \times 10^{6} \mathrm{~J} / \mathrm{kg}\)

A \(10.0-\mu \mathrm{F}\) capacitor is fully charged across a \(12.0-\mathrm{V}\) battery. The capacitor is then disconnected from the battery and connected across an initially uncharged capacitor with capacitance \(C\). The resulting voltage across each capacitor is \(3.00 \mathrm{~V}\). What is the value of \(C ?\)

Four point charges each having charge Qare located at the corners of a square having sides of length \(a\). Find symbolic expressions for (a) the total electric potential at the center of the square due to the four charges and (b) the work required to bring a fifth charge \(q\) from infinity to the center of the square.

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