Question 1

Which of the following best explains why a person's hair stands on end during a thunderstorm, as shown in the first image?

Accepted Answer

The presence of a large electric field causes charge separation, resulting in repulsion between similarly charged hair strands.

Question 2

In the diagram showing electric field lines between two parallel plates, what does the density of field lines indicate about the magnitude of the electric field at points A and C?

Accepted Answer

The electric field magnitude is greater where the field lines are closer together.

Question 3

Given a uniformly charged rod of length $$L$$ and total charge $$Q$$, what is the linear charge density $$\lambda$$?

Accepted Answer

$$\lambda = \frac{Q}{L}$$

Question 4

For a uniformly charged surface of area $$A$$ and total charge $$Q$$, what is the surface charge density $$\eta$$?

Accepted Answer

$$\eta = \frac{Q}{A}$$

Question 5

A semi-circular rod has charge $$+Q$$ distributed along the top and $$-Q$$ along the bottom. What is the direction of the net electric field at the center?

Accepted Answer

Downward, due to the vertical components of the field from each segment adding up.

Question 6

A point charge $$q is $$located at $$(0, y_0$) on $$the $$y-$$axis. What is the $$x-$$component of the electric field at point $$(x_p, 0) on $$the $$x-$$axis?

Accepted Answer

$$E_x = \frac{1}{4\pi\$$epsilon_0$$} \frac{q x_p}{(x_p^2$ + y_0$^2$$)^{3/2}$$}$$

Question 7

For a line of charge of length $$l$$ and total charge $$q$$ along the $$y-$$axis, what is the expression for the $$x-$$component of the electric field at point $$P at$$ $$(x_p, 0)$$?

Accepted Answer

$$E_x = \frac{1}{4\pi\$$epsilon_0$$} \int_{-l/2}^{l/2} \frac{q x_p}{l (x_p^2$ + y^2$)^{3/2}$$} dy$

Question 8

What is the magnitude of the electric field at a distance $$r$$ from an infinitely long line with uniform charge density $$\lambda$$?

Accepted Answer

$$E = \frac{\lambda}{2\pi\$$epsilon_0$$ r}$$

Question 9

For a parallel-plate capacitor with plates of area $$A$$ and separation $$d$$, what is the magnitude of the electric field between the plates if the charge on each plate is $$Q$$?

Accepted Answer

$$E = \frac{Q}{\$$epsilon_0$$ A}$$

Question 10

A charged particle of mass $$m$$ and charge $$q is $$placed in a uniform electric field $$E. $$What is its acceleration?

Accepted Answer

$$a = \frac{q E}{m}$$

Question 11

If a negatively charged particle is placed in a uniform electric field, in which direction does it accelerate?

Accepted Answer

Opposite to the direction of the electric field.

Question 12

Which of the following is true about the electric field outside a parallel-plate capacitor?

Accepted Answer

The electric field is approximately zero outside the plates.

Question 13

For a sphere of radius $$R$$ with uniformly distributed charge $$Q$$, what is the electric field at a distance $$r \u003e R$$ from the center?

Accepted Answer

$$E = \frac{1}{4\pi\$$epsilon_0$$} \frac{Q}{r^2$}$$

Question 14

A plane has a uniform surface charge density $$\eta. $$What is the magnitude of the electric field just above the surface?

Accepted Answer

$$E = \frac{\eta}{2\$$epsilon_0$$}$$

Question 15

A ring of radius $$R$$ carries a total charge $$Q. $$What is the electric field at a point on the axis passing through the center of the ring, at a distance $$z$$ from the center?

Accepted Answer

$$E = \frac{1}{4\pi\$$epsilon_0$$} \frac{Q z}{(z^2$ + R^2$)^{3/2}$$}$

Question 16

If the electric field at a point is zero, which of the following must be true about the field lines at that point?

Accepted Answer

There are no field lines passing through that point.

Question 17

Which mathematical operation is used to calculate the total electric field from a continuous charge distribution?

Accepted Answer

Integration over all infinitesimal charge elements.

Question 18

A parallel-plate capacitor is constructed with plates of area $$A$$ and separation $$d. If $$the charge on the plates is doubled, what happens to the electric field between the plates?

Accepted Answer

The electric field doubles.

Electric Fields and Continuous Charge Distributions

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