Question 1

A point charge +q and a point charge -q are separated by a distance 2a, forming an electric dipole centered at the origin. Using the equation for the potential due to a single point charge, what is the approximate electric potential $$V_R at a $$point R located a distance $$x$$ from the dipole center along the x-axis, as $$x$$ tends towards infinity?

Accepted Answer

$$V_R \approx -\frac{2qa}{4\pi \$$epsilon_0$$ x^2$}$$

Question 2

An electron is released from rest at a distance $$x = 1.0\ \mathrm{m}$$ from a fixed dipole with $$q = 1\ \mathrm{nC}$$ and $$a = 0.1\ \mathrm{mm}. $$What is the electron’s speed when it is a distance $$x = 2.0\ \mathrm{m}$$ from the dipole? (Neglect gravity and use $$e = 1.6 	imes 10$$^{-19}$$\ \mathrm{C}$$, $$m_e = 9.11 	imes 10$$^{-31}$$\ \mathrm{kg})$$

Accepted Answer

$$v = \sqrt{\frac{4qa e}{4\pi \$$epsilon_0$$ m_e} \left( \frac{1}{x_1$^2} - \frac{1}{x_2$^2} \right)}$$

Question 3

In the circuit shown, what is the current through the $$3\ \Omega$$ resistor?

Accepted Answer

The current is found by applying Kirchhoff's rules. $$I = 1.5\ \mathrm{A}$$

Question 4

A long straight wire carries a current $$i_1$$ and a rectangular loop a distance $$a$$ away, with sides of length $$b$$ and $$c$$, carries a current $$i_2. $$What is the net force on the loop due to $$i_1$$?

Accepted Answer

$$F = \frac{\mu_0$ i_1$ i_2$ b}{2\pi} \left( \frac{1}{a} - \frac{1}{a+c} \right)$$

Question 5

A solenoid has $$N = 1000$$ turns uniformly distributed over a length $$\ell = 40.0\ \mathrm{cm}. $$What current is needed to produce a magnetic field of $$1.00 	imes 10$$^{-4}$$\ \mathrm{T} at $$its centre?

Accepted Answer

$$I = \frac{B \ell}{\mu_0$ N}$$

Question 6

For a solenoid, $$L = \frac{N \Phi_B}{I}. $$What does $$L$$ signify?

Accepted Answer

The inductance of the solenoid

Question 7

Unpolarized light passes through three polarizers with axes at $$0^\circ$$, $$60^\circ$$, and $$90^\circ. $$What fraction of the initial intensity $$I_0$$ emerges from the system?

Accepted Answer

$$I = \frac{I_0$}{8}$$

Question 8

If Polarizer 2 is removed from the three-polarizer system, what fraction of $$I_0$$ emerges from the system?

Accepted Answer

$$I = 0$$

Question 9

A transformer operates at $$V_p = 8.5\ \mathrm{kV} on $$the primary side and supplies $$V_s = 120\ \mathrm{V} on $$the secondary side. What is the turns ratio $$\frac{N_p}{N_s}$$?

Accepted Answer

$$\frac{N_p}{N_s} = \frac{V_p}{V_s}$$

Question 10

The average rate of energy consumption in the houses served by the transformer is $$18\ \mathrm{kW}. $$What is the rms current in the secondary coil?

Accepted Answer

$$I_s = \frac{P}{V_s}$$

Question 11

A convex mirror forms an image of an object Y. Is the image real or virtual?

Accepted Answer

Virtual

Question 12

For the convex mirror, is the image larger or smaller than the object?

Accepted Answer

Smaller

Question 13

Monochromatic light of wavelength $$\lambda = 620\ \mathrm{nm}$$ passes through a slit $$0.450\ \mathrm{mm}$$ wide. The diffraction pattern is observed on a screen $$3.00\ \mathrm{m}$$ away. At what distance from the center of the central maximum does the first minimum occur?

Accepted Answer

$$y = \frac{\lambda L}{a}$$

Question 14

Which of the following positions are within the central maximum for the single-slit diffraction pattern described above?

Accepted Answer

Positions with $$|y| \u003c \frac{\lambda L}{a}$$

Question 15

A charged particle moves with velocity $$\vec{v}$$ perpendicular to a uniform magnetic field $$\vec{B}. $$What is the radius of its circular path?

Accepted Answer

$$r = \frac{mv}{|q|B}$$

Question 16

A parallel-plate capacitor is filled with a dielectric of constant $$K. $$What is the new capacitance?

Accepted Answer

$$C = K \$$epsilon_0$$ \frac{A}{d}$$

Physics II for Engineers: Step-by-Step Study Guidance

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