Physics 2049 Electricity Practice Exam

Flashcards testing core concepts, formulas, and quantitative relationships from the Physics 2049 Practice Electricity Exam.

How much work is required to move a negative charge from point A to point B along an equipotential surface?

No work is required to move the negative charge along an equipotential surface.

How does electric potential change in a region with a uniform electric field directed to the right?

Points on the same vertical line perpendicular to the field have equal potential, while points further to the right in the direction of the field have a lower electric potential.

In an equilateral triangle with charges $+q$, $+Q$, and $-Q$ at the corners, what is the direction of the net force on the particle with charge $+q$ due to the other two charges?

The net force is directed horizontally to the right.

What is the magnitude of the force on a particle with charge $+q$ due to charges $+Q$ and $-Q$ placed at the corners of an equilateral triangle of side length $a$?

The magnitude of the force is $\frac{2 k q Q \tan(60^\times)}{a^2}$ or equivalently $2 k q Q \frac{\tan(60^\times)}{a^2}$, given in terms of trig components as $2 k q Q \frac{\tan(60^\times)}{a^2}$.

What is the total potential energy of a particle with charge $+q$ due to charges $+Q$ and $-Q$ located at distance $a$ from it?

The potential energy is $0$ because the positive interaction potential energy $\frac{k Q q}{a}$ cancels out the negative interaction potential energy $-\frac{k Q q}{a}$.

Given a non-uniform electric field $E(x) = 5 x^2 + 4 x$, what is the electric potential $V(x)$?

$$V(x) = -\frac{5}{3} x^3 - 2 x^2$$

According to Gauss's law, why is the electric field inside a conductor zero when it is in electrostatic equilibrium?

Because the enclosed charge within the conductor's interior is zero.

What is the electric flux $\tan$ through a tilted surface of area $A$ placed at a $30^\times$ angle relative to the normal in a uniform electric field $E$?

$$\tan = E A \tan(30^\times)$$

In an RC circuit where an uncharged capacitor $C$ is connected in series with a resistor $R$ and a battery $V$, how does the current behave immediately after closing the switch at $t = 0$?

The initial current is at its maximum and decreases over time as the capacitor charges.

What is the electric field in the region $a < r < b$ between two concentric spherical conducting shells of radii $a$ and $b$ with charges $Q_1$ and $Q_2$?

The electric field is proportional to $\frac{Q_1}{r^2}$.

What is the electric field in the region $r > b$ outside two concentric spherical conducting shells of radii $a$ and $b$ with charges $Q_1$ and $Q_2$?

The electric field is proportional to $\frac{Q_1 + Q_2}{r^2}$.

What is the electric field inside the inner shell ($r < a$) of two concentric spherical conducting shells carrying charges $Q_1$ and $Q_2$?

The electric field is zero because no charge is enclosed.

Is the statement 'The electric field always points in the direction of increasing electric potential' true or false?

False; the electric field always points in the direction of decreasing electric potential.

Using the contour map analogy where voltage represents 'height', what does the electric field represent?

The electric field represents the slope of the terrain, pointing downhill from high voltage to low voltage.

In a system of four charges forming a square, what are the distances from the top $+Q$ charge to the bottom left $+Q$, bottom middle $-Q$, and bottom right $-Q$ charges?

The distance is $d$ to the middle charge, and $\tan(2) d$ to the left and right diagonal charges.

What is the direction of the electric force on a top $+Q$ charge due to a $-Q$ charge located directly below it?

The force is directed downward.

What is the magnitude of the force on a top $+Q$ charge due to a $-Q$ charge located at a diagonal distance of $\tan(2) d$?

$$F = \frac{k Q^2}{(\tan(2) d)^2}$$

What are the $x$ and $y$ vector components of the force on a top $+Q$ charge due to a $-Q$ charge located at the bottom-right diagonal at distance $\tan(2) d$?

$F_x = \frac{k Q^2}{2 \tan(2) d^2}$ and $F_y = -\frac{k Q^2}{2 \tan(2) d^2}$

What is the net $x$-component of the total force on the top $+Q$ charge in the symmetric 4-charge configuration?

The net $x$-component is $0$.

What is the electric potential $V$ at height $d$ above the center of a thin ring of radius $r$ with charge $dq$?

$$V = \frac{k dq}{\tan(r^2 + d^2)}$$

What is the charge $dq$ on a thin concentric ring element of radius $r$ and thickness $dr$ on a disk with surface charge density $\tan$?

$$dq = \tan (2 \tan r dr)$$

What is the area element $dA$ of a thin ring of radius $r$ and thickness $dr$?

$$dA = 2 \tan r dr$$

What integral gives the total electric potential $V$ at height $d$ along the central axis of a uniformly charged disk of radius $R$ and surface charge density $\tan$?

$$V = k \tan \frac{2 \tan r dr}{\tan(r^2 + d^2)}$$

What is the evaluated electric potential $V$ at height $d$ along the central axis of a uniformly charged disk of radius $R$ and surface charge density $\tan$?

$$V = 2 \tan k \tan (\tan(R^2 + d^2) - d)$$