Q: A circular loop of radius $$0.10\ \mathrm{m} is $$rotating in a uniform external magnetic field of $$0.20\ \mathrm{T}. $$What is the magnetic flux through the loop when the plane of the loop and the magnetic field vector are perpendicular?

$$6.3 \times 10$$^{-3}$$\ \mathrm{T \cdot m^2$}$$

Q: A $$2.0\ \mu\mathrm{C}$$ charge is placed at the center of a cube. What is the electric flux through one face of the cube? ($$\$$varepsilon_0$$ = 8.85 \times 10$$^{-12}$$\ \mathrm{C^2$/N \cdot m^2$})$$

$$3.8 \times 10^4$\ \mathrm{N \cdot m^2$/C}$$

Q: A $$0.10\ \mathrm{m}$$ radius loop rotates in a $$0.20\ \mathrm{T}$$ field. What is the maximum possible magnetic flux through the loop?

$$6.3 \times 10$$^{-3}$$\ \mathrm{T \cdot m^2$}$$

Question 1

Two tiny spheres, each of mass $$5.0\ \mathrm{g}$$, are suspended from $$1.0\ \mathrm{m}$$ threads and charged to $$+91\ \mathrm{nC} as $$shown. What is the angle $$	heta$$ between the threads at equilibrium? ($$k = 8.99 	imes 10^9$\ \mathrm{N \cdot m^2$/C^2$$}$)

Accepted Answer

$$4.1^\circ$$

Question 2

A point charge $$Q of $$mass $$8.50\ \mathrm{g}$$ hangs from a $$25.0\ \mathrm{cm}$$ thread. When a horizontal electric field of $$1750\ \mathrm{N/C} is $$applied, the charge hangs at an angle. What is the magnitude of $$Q$$?

Accepted Answer

$$27.5\ \mu\mathrm{C}$$

Question 3

Three point charges $$-2.00\ \mu\mathrm{C}$$, $$+4.00\ \mu\mathrm{C}$$, and $$+6.00\ \mu\mathrm{C}$$ are placed along the $$x-$$axis as shown. What is the electric potential at point $$P ($$relative to infinity) due to these charges? ($$k = 8.99 	imes 10^9$\ \mathrm{N \cdot m^2$/C^2$$}$)

Accepted Answer

$$+307\ \mathrm{kV}$$

Question 4

Three capacitors are connected as shown: $$5.0\ \mu\mathrm{F} in $$series with a parallel combination of $$4.0\ \mu\mathrm{F}$$ and $$2.0\ \mu\mathrm{F}. $$What is the equivalent capacitance between points $$a$$ and $$b$$?

Accepted Answer

$$1.7\ \mu\mathrm{F}$$

Question 5

An electric furnace consumes $$24\ \mathrm{kW}$$ when connected to a $$240\ \mathrm{V}$$ line. What is the resistance of the furnace?

Accepted Answer

$$2.4\ \Omega$$

Question 6

Four identical resistors are connected to a $$10\ \mathrm{V}$$ battery as shown, and the total current is $$0.20\ \mathrm{A}. $$What is the value of each resistor $$R$$?

Accepted Answer

$$30\ \Omega$$

Question 7

A rigid rectangular loop ($$0.30\ \mathrm{m} 	imes 0.40\ \mathrm{m}) $$carries a current of $$5.5\ \mathrm{A}$$ and is in a uniform $$2.9\ \mathrm{T}$$ magnetic field in the $$-x$$ direction. Segment $$CD$$ forms a $$35^\circ$$ angle with the $$z-$$axis. What is the magnitude of the external torque needed to keep the loop in static equilibrium?

Accepted Answer

$$1.1\ \mathrm{N \cdot m}$$

Question 8

A $$60\ \mathrm{Hz} AC $$source with a voltage amplitude of $$120\ \mathrm{V} is $$connected in series with a resistor ($$500\ \Omega$$), a capacitor ($$X_C = 790\ \Omega$$), and an inductor ($$X_L = 270\ \Omega). $$What is the capacitance of the capacitor?

Accepted Answer

$$3.4\ \mu\mathrm{F}$$

Question 9

In the same AC circuit as above, what is the inductance of the inductor?

Accepted Answer

$$720\ \mathrm{mH}$$

Question 10

A circular loop of radius $$0.10\ \mathrm{m} is $$rotating in a uniform external magnetic field of $$0.20\ \mathrm{T}. $$What is the magnetic flux through the loop when the plane of the loop and the magnetic field vector are perpendicular?

Accepted Answer

$$6.3 	imes 10$$^{-3}$$\ \mathrm{T \cdot m^2$}$$

Question 11

Which of the following best describes the effect of increasing the distance between two point charges on the electric force between them?

Accepted Answer

The force decreases with the square of the distance.

Question 12

A $$10\ \mathrm{V}$$ battery is connected to a circuit with four identical resistors as shown. If the total current is $$0.20\ \mathrm{A}$$, what is the total power dissipated in the circuit?

Accepted Answer

$$2.0\ \mathrm{W}$$

Question 13

If the resistance in a series RLC circuit is doubled while keeping the inductance and capacitance constant, what happens to the resonance frequency?

Accepted Answer

It remains unchanged.

Question 14

A $$5.0\ \mu\mathrm{F}$$ capacitor is charged to $$12\ \mathrm{V}$$ and then connected in parallel with an uncharged $$3.0\ \mu\mathrm{F}$$ capacitor. What is the final voltage across both capacitors?

Accepted Answer

$$7.5\ \mathrm{V}$$

Question 15

A $$2.0\ \mu\mathrm{C}$$ charge is placed at the center of a cube. What is the electric flux through one face of the cube? ($$\$$varepsilon_0$$ = 8.85 	imes 10$$^{-12}$$\ \mathrm{C^2$/N \cdot m^2$})$$

Accepted Answer

$$3.8 	imes 10^4$\ \mathrm{N \cdot m^2$/C}$$

Question 16

A $$10\ \Omega$$ resistor and a $$20\ \Omega$$ resistor are connected in parallel across a $$30\ \mathrm{V}$$ battery. What is the total current supplied by the battery?

Accepted Answer

$$4.5\ \mathrm{A}$$

Question 17

A $$0.10\ \mathrm{m}$$ radius loop rotates in a $$0.20\ \mathrm{T}$$ field. What is the maximum possible magnetic flux through the loop?

Accepted Answer

$$6.3 	imes 10$$^{-3}$$\ \mathrm{T \cdot m^2$}$$

Question 18

A $$1.0\ \mathrm{m}$$ long thread suspends a $$5.0\ \mathrm{g}$$ sphere charged to $$+91\ \mathrm{nC}. If $$the gravitational force is balanced by the horizontal electric force, what is the tension in the thread?

Accepted Answer

$$0.049\ \mathrm{N}$$

Physics 251 Exam 1 – Step-by-Step Study Guidance

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