Model Electric and Magnetic Fields - Physics

1. What is the direction of the electric field around a positive point charge?

   Radially outward from the charge. Field lines point away from positive charges.

2. What is the relationship between uniform electric field and potential difference over distance $d$?

   $E = \frac{\Delta V}{d}$. In uniform fields, voltage drop is proportional to distance.

3. What is the definition of magnetic force on a moving charge $q$ with speed $v$ in field $B$?

   $F = qvB\sin(\theta)$. Lorentz force depends on velocity, field, and angle between them.

4. What is the electric field magnitude produced by a point charge $Q$ at distance $r$?

   $E = k\frac{|Q|}{r^2}$. Combines Coulomb's law with $E = F/q$ for a point charge field.

5. What is the direction rule for magnetic force on a positive charge moving in a magnetic field?

   Right-hand rule for $\vec{F} = q\vec{v}\times\vec{B}$. Fingers follow $\vec{v}$, curl to $\vec{B}$, thumb shows $\vec{F}$.

6. What is the value of the permeability of free space $\mu_0$ (exact in SI form)?

   $\mu_0 = 4\pi\times 10^{-7}\ \text{T}\cdot\text{m}/\text{A}$. Fundamental constant relating magnetic field to current.

7. What is the equation for the electric force on a charge $q$ placed in an electric field $E$?

   $F = qE$. Force equals charge times field strength.

8. Identify the rule that determines the direction of induced current opposing the change in magnetic flux.

   Lenz's law. Induced effects oppose the change causing them.

9. What is the magnetic force magnitude on a straight wire of length $L$ carrying current $I$ in field $B$ at angle $\theta$?

   $F = ILB\sin\theta$. Current is moving charge; force maximized when wire perpendicular to field.

10. What is the magnetic force magnitude on a straight wire of length $L$ carrying current $I$ in field $B$?

    $F = ILB\sin(\theta)$. Current $I$ is moving charge; replaces $qv$ in force formula.

11. What is the magnetic force magnitude on a charge $q$ moving at speed $v$ in field $B$ at angle $\theta$?

    $F = |q|vB\sin\theta$. Lorentz force law: maximum when motion is perpendicular to field.

12. What is the magnetic field magnitude at distance $r$ from a long straight wire carrying current $I$?

    $B = \frac{\mu_0 I}{2\pi r}$. Ampère's law result for infinite straight wire.

13. What is the magnetic field magnitude at the center of a single circular loop of radius $R$ carrying current $I$?

    $B = \frac{\mu_0 I}{2R}$. Biot-Savart law result for loop center.

14. What is the radius of circular motion for a charge $q$ moving perpendicular to uniform $B$ with speed $v$ and mass $m$?

    $r = \frac{mv}{|q|B}$. Centripetal force from magnetic force balances circular motion.

15. What is the relationship between electric potential difference and potential energy change?

    $\Delta V = \frac{\Delta U}{q}$. Potential is energy per unit charge.

16. Which option gives the direction of magnetic force on a positive charge: $\vec{F} = q\vec{v}\times\vec{B}$?

    Right-hand rule for $\vec{v}\times\vec{B}$; reverse for negative $q$. Cross product gives force direction; thumb points along $\vec{F}$ for positive charge.

17. What is the work done by the electric field when a charge moves through potential difference $\Delta V$?

    $W_{\text{field}} = -q\Delta V$. Negative sign: field does positive work when charge moves to lower potential.

18. Identify the net electric field direction at the midpoint between equal positive charges $+Q$ and $+Q$.

    Zero; the fields cancel at the midpoint. Equal charges create equal opposing fields at midpoint.

19. What is the definition of electric potential difference (voltage) in terms of work and charge?

    $\Delta V = \frac{\Delta U}{q}$. Voltage is work per unit charge moved between points.

20. What is the direction of the electric force between two charges with the same sign?

    Repulsive; each force points away from the other charge. Like charges repel according to Coulomb's law.

21. What is the magnetic force on a charge moving parallel to a magnetic field (any nonzero $v$)?

    $F = 0$. $\sin(0°) = 0$ when velocity is parallel to field.

22. What is the electric potential due to a point charge $Q$ at distance $r$?

    $V = k\frac{Q}{r}$. Potential decreases linearly with distance from point charge.

23. What is the value of Coulomb's constant $k$ in vacuum (to $3$ significant figures)?

    $k = 8.99\times 10^9\ \text{N}\cdot\text{m}^2/\text{C}^2$. This constant relates charge, distance, and force in Coulomb's law.

24. What is the direction of magnetic field lines around a straight current-carrying wire?

    Concentric circles given by the right-hand grip rule. Thumb along current, fingers curl in field direction.

25. What is the electric field magnitude between parallel plates with potential difference $\Delta V$ and separation $d$?

    $E = \frac{\Delta V}{d}$. Uniform field between plates equals voltage gradient.

26. What is the electric force magnitude between two point charges separated by distance $r$?

    $F = k\frac{|q_1 q_2|}{r^2}$. Coulomb's law: force is proportional to charge product and inversely to distance squared.

27. What is the formula for electric potential energy of two point charges separated by distance $r$?

    $U = k\frac{q_1 q_2}{r}$. No $r^2$ in denominator; energy, not force.

28. What is the direction of electric field lines relative to equipotential lines?

    Perpendicular to equipotential lines. Field points from high to low potential, perpendicular to constant potential surfaces.

29. What is the formula for the electric force magnitude between two point charges?

    $F = k\frac{|q_1 q_2|}{r^2}$. Coulomb's law: force is proportional to charge product and inversely to distance squared.

30. What is the electric potential energy of two point charges separated by distance $r$?

    $U = k\frac{q_1 q_2}{r}$. Energy is proportional to charge product, inversely to separation.

31. What is Faraday's law for the induced emf in a loop with $N$ turns and changing flux $\Phi_B$?

    $\mathcal{E} = -N\frac{d\Phi_B}{dt}$. Changing flux induces emf; negative sign from Lenz's law.

32. What is the definition of electric field magnitude $E$ in terms of force on a test charge?

    $E = \frac{F}{q}$. Electric field is force per unit charge on a test charge.

33. Which option gives the direction of force on an electron moving right in a magnetic field into the page?

    Downward. Right-hand rule: $\vec{v}$ right, $\vec{B}$ in gives $\vec{F}$ up; electron reverses to down.

34. What is the magnetic flux through a flat area $A$ in uniform field $B$ at angle $\theta$ to the area normal?

    $\Phi_B = BA\cos\theta$. Flux is field component perpendicular to surface times area.

35. What is the definition of electric field at a point in terms of force and test charge?

    $\vec{E} = \frac{\vec{F}}{q}$. Field is force per unit positive test charge.

36. Identify the net electric field direction at the midpoint between charges $+Q$ (left) and $-Q$ (right).

    To the right, toward $-Q$. Both charges' fields point right at midpoint, adding up.

37. What is the direction of the electric field around a negative point charge?

    Radially inward toward the charge. Field lines point toward negative charges.

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