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Magnetic Fields and Electromagnetic Induction
Lenz's Law
Lenz's Law states that states that the direction of the electric current which is induced (influenced ) by a changing magnetic field while it is in a conductor
has to be oriented in a way the the induced current opposes the initial changing magnetic field.
1) A stationary coil is in a magnetic field that is changing with time. Does the emf induced in the coil depend on the actual values of the magnetic field?
The electromagnetic force ε = - N d Φ /dt, Φ = BAcos θ
Therefore the emf => is the change in the magnetic field over time, the value of the magnetic field will only give us a linear relationship with the magnetic field field. The greater the strength of it the greater the emf.
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Capacitors and Capacitance
8.1 Does the capacitance of a device depend on the applied voltage? Does the capacitance of a device depend on the charge residing on it?
The charge stored in the capacitor doesn't depend on the applied voltage, the charge stored in it depends upon applied voltage and the charge stored in applied voltage is Q=VC. The greater the voltage applied to any capacitor, the greater the charge stored in it. The amount of charge depends on the physical characteristics like its size and the applied voltage.
8.3 The value of the capacitance is zero if the plates are not charged. True or false?
The capacitance of a capacitor does depend on the surface area of the capacitor plate, the separation between the plates and the dielectric material filled inside the plates.
The capacitance of any capacitor is fixed, it will not increase or decrease.
8.5 Does the capacitance of a spherical capacitor depend on which sphere is charged positively or negatively?
8.7 What is the maximum capacitance you can get by connecting three 1.0-μF1.0-μF capacitors? What is the minimum capacitance?
8.9 Discuss what would happen if a conducting slab rather than a dielectric were inserted into the gap between the capacitor plates.
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Potential Difference and Electrical Potential Energy
Conceptual Questions
7.7 Voltage is the common word for potential difference. Which term is more descriptive, voltage or potential difference?
Voltage and potential difference are defined as the work done to bring in a referenced charge to another reference point. The terms are defined as the flow of charges across a material or conductor. One difference is that voltage is used to define the potential of a point with respect to the potential point.
7.9 What is the relationship between voltage and energy? More precisely, what is the relationship between potential difference and electric potential energy?
Potential difference is given by V = U/q , where V = Kq/r
Electric potential Energy U = qV , thus U = KQq/r
Where the Potential difference is the energy/per unit charge and Electric potential energy is Voltage times charge.
7.15 In What region of space is the potential due to a uniformly charged sphere the same as that of a point charge and in what region does it differ from that of a point charge.?
Using Guass’s and spherical symmetry , We that the potential at a distance R depends only on the charge that is inside the sphere. (R) . When we have a radius R that is smaller than the radius of r=infinity, there will be no charge inside the sphere. When r > R ( Greater than the radius of sphere all the charge is inside the sphere just like a point charge.
7.17 If the electric field is zero(0) through a region, must the electric potential also be zero (0) in the region?
The equation is E=∆V/d,
where E = 0, thus rearranging the
Ed=∆V => 0*d = ∆V
∆V = 0
Thus the electric potential must also be 0 in this region.
7.19 If two points are at the same potential are there any electric field lines connecting them?
Looking at equipotential surfaces we see that the two points do not need to be near each other to lie on the same equipotential line. Thus the electric field do not have to have the same electric field line connecting them, however may come from the same electrical source and be the same distance away.
7.21 Is the electric potential necessarily constant over the surface of a conductor?
For static electric fields and conductors there is a rule that the electric field must be perpendicular towards the surface of a conductor. Implying that a conductor becomes an equipotential surface during static situations. Thus there can be no voltage difference across the surface of a conductor, or charges will flow.
7.23 Can a positively charged conductor be at a negative potential? Explain.
Yes , a positively charged conductor can be at a negative potential. In order for this to work we can imagine a positively charged conductor being placed at/in a negatively charged equipotential. If the positively charged conductor has a greater net charge than the static negative equipotential the remaining charge on the conductor will continue to be positive.
7.25 (Applications of Electrostatics) Why Are the metal support rods for satellite network dishes generally grounded?
The reason metal rods are grounded is to protect the equipment from lightning strikes. What grounding does is allow the excess charge to flow through the rod into earth.
7.27 ( Applications of Electrostatics) What are the similarities and differences between the processes in a photocopier and an electrostatic precipitator?
Both are used to create copies the major differences between Photocopiers and electrostatic precipitators processes is that in electrostatic copying, there is a limitless photoconducting surface that is excluded from the machine and the copy paper is specially treated to pick up the toner.
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