After rubbing a balloon on dry hair, the balloon sticks to a wall. Explain why the balloon becomes charged.

A small positive test charge is placed near a charged object and begins to move. What does this observation best show about the region around the charged object?

Several point charges are placed near a point in space. Each charge produces an electric field at that point. According to the principle of superposition, how is the net electric field at that point determined?

A long wire has charge density $$\lambda=3.0\times10^{-6}\,\text{C/m}$$ . A point is located at a distance $$r=0.20\,\text{m}$$ from the wire. The permittivity of free space is $$\varepsilon_0=8.85\times10^{-12}\,\text{C}^2/(\text{N}\cdot\text{m}^2)$$ . Which statement correctly describes the electric field at this point due to the wire?

A teacher wants to demonstrate charging by induction using a metal sphere, a charged rod, and a grounding wire. Which procedure correctly demonstrates charging by induction?

Two point charges are placed 0.50 m apart: q1 = +2 μC and q2 = −3 μC. What is the magnitude of the electric force between them?

A positive test charge is placed at different points around a negative charge. At which point will the electric field be strongest?

A point charge of +3.0 μC is fixed in space. A point is located 0.20 m away from the charge. Using Coulomb’s law, what is the electric field at that point, including its direction?

A uniform electric field of E = $$200\ \frac{N}{C}$$ passes through a flat rectangular sheet with area A = $$0.5\ m^2$$ . The sheet is tilted at an angle $$\theta$$ relative to the field. What is the electric flux through the sheet if the tilt angle is $$\theta=60^0$$ ?

A sphere of radius 0.10 m carries a total charge of 4.0 μC uniformly distributed throughout its volume. Calculate the magnitude of the electric field at a point 0.05 m from the center of the sphere (inside the sphere).

A charge of q = 5 μC is moved across a potential difference of 120 V. What is the work done on the charge?

A charge Q = $$40.0\times10^{-12}$$ C is uniformly distributed on a plastic sphere of 0.005 m radius. Find the electric potential at its surface when k = $$8.99\times10^{9}$$ N·m^2/C^2.

A set of equipotential lines is drawn around a metal sphere. The equipotential surfaces are perfect concentric circles, with values: 80 V (closest to sphere), 60 V, 40 V, 20 V. The equipotential lines are closest near the sphere and farther apart as you move away. Based on the equipotential lines, what is the direction of the electric field around the sphere?

The electric potential along x-axis is given by $$V(x)=8x-4$$ where V is in volts and x is in meters. Find the electric field in the region.

The electric potential along x-axis is given by  where V〈x〉=8x -4 is in volts and x in meters. what is the magnitude and direction of the electric field in this region?

A parallel-plate capacitor has plates of area $$A=0.02\,\text{m}^2$$ separated by $$d=0.01\,\text{m}$$ . If the plate area is doubled while keeping the separation and voltage the same, which of the following occurs?

Find the equivalent capacitance of the series when three capacitors $$C_1=10\,\mu\text{F}$$ , $$C_2=10\,\mu\text{F}$$ , and $$C_3=12\,\mu\text{F}$$ are connected.

A digital camera uses a capacitor system to store energy for its flash. Two capacitors with capacitances $$2.0\times10^{-6}\,\text{F}$$ and $$3.0\times10^{-6}\,\text{F}$$ are connected in series to a 100 V battery. What is the total charge of the system?

Two students rub different objects: • Student 1 rubs a plastic comb with dry hair. • Student 2 rubs a glass rod with silk. Both objects become charged. Which conclusion best explains this observation?

During an induction experiment, a positively charged rod is brought near a neutral metal sphere. Electrons move toward the side near the rod. What does this observation show?

Three point charges lie on a straight line at positions

• q1=+4.0 μC at x=0.00 m

• q2=−2.0 μC at x=0.30 m

• q3=+3.0 μC at x=0.70 m

Explains the direction of the net force on q2.

Two regions have electric fields of different strengths. Which conclusion is most reasonable?

Two positive point charges lie on the x-axis:

• Q1=+4.0 μC at x=0.00 m

• Q2=+3.0 μC at x=0.40 m

Point P is located at the midpoint, x=0.20 m. The electric field at P due to each charge is calculated, and the net electric field is found to be directed to the right. Which statement best explains why the net electric field points to the right?

A charge Q = $$40.0\times10^{-12}$$ C is uniformly distributed on a plastic sphere of 0.005 m radius when k = $$8.99\times10^9N·m^2/C^2.$$ Explains the effect of this potential on a positive test charge near the sphere.

You observe an oddly shaped metal object with equipotential lines very close together near a sharp tip and widely spaced in smoother regions of the object. Based on the equipotential lines, what can be inferred about the electric field around the object?

The electric potential in a region is given by $$V(x,y)=4x+2y$$ and the electric field is related to the potential by $$\vec{E}=-\left(\frac{\partial V}{\partial x}\,\hat{i}+\frac{\partial V}{\partial y}\,\hat{j}\right)$$ . Which statement correctly describes the electric field vector in this region?

The electric potential in a region is $$V(x)=3x^2-6x$$ and the electric field is related to the potential by $$E_x=-\frac{dV}{dx}$$ . At x = 1.0 m, which statement correctly describes the electric field?

A cylindrical capacitor has a length L and radius R. If the distance between the cylinders is increased, which statement explains the capacitor’s behavior?

A technician is checking a circuit board where three capacitors (10 µF, 10 µF, and 12 µF) are connected in parallel to improve energy storage. Which statement correctly explains the equivalent capacitance of the circuit?

A student claims: “The net electric force on a charge is always zero if there are charges on both sides.” Which evaluation is most accurate?

A simplified one-dimensional model of a lithium atom is shown:

·      A nucleus with the charge $$q_1=+3.0e$$  at $$x=0.00m$$ ;

·      Two electrons, each with charge $$q_2=q_3=-1.6\times10^{-19}C$$  ,  are located at   $$x=1.0\times10^{-10}m$$ and $$x=-1.0\times10^{-10}m$$ ;  and

·      Point P is at $$x=2.0\times10^{-10}m$$ .

After calculating the electric field at point P, a student concludes that the net electric field points to the left because the electrons produce a stronger electric field than the nucleus. Evaluate the student’s conclusion. Explain whether it is correct or incorrect and justify your reasoning.

A uniform electric field of $$E=150\,\text{N/C}$$ passes through a square sheet with area $$A=0.4\,\text{m}^2$$ . Four students calculated the flux when the sheet is tilted at $$\theta=40^\circ$$ :

• Student 1: $$\Phi_E=60\,\text{N}\cdot\text{m}^2/\text{C}$$

• Student 2: $$\Phi_E=50\,\text{N}\cdot\text{m}^2/\text{C}$$

• Student 3: $$\Phi_E=80\,\text{N}\cdot\text{m}^2/\text{C}$$

• Student 4: $$\Phi_E=42.4\,\text{N}\cdot\text{m}^2/\text{C}$$

Which student’s answer is correct?

A large, flat, non-conducting plate has a uniform surface charge density of $$8.0\,\mu\text{C/m}^2$$ . Four students calculate the electric field near the plate: . Who correctly calculated the electric field?

Which statement CORRECTLY interpret the potential energy change?

A metal sphere has a charge of $$6.0\times10^{-12}\,\mathrm{C}$$ and a radius of $$0.010\,\mathrm{m}$$ . The electric potential at the surface of a charged sphere is given by $$V=\dfrac{kQ}{r}$$ where $$k=8.99\times10^{9}\,\mathrm{N\,m^{2}/C^{2}}$$ . Which conclusion BEST explains the electric potential at the surface and how the sphere’s charge affects it?

Between two nearby plates, the equipotential lines appear as evenly spaced vertical lines labeled 100 V, 90 V, 80 V, 70 V, …, decreasing toward one plate. Which conclusion BEST describes the electric field between the plates?

A spherical capacitor has its radius doubled and a dielectric slab is added between the spheres. Which conclusion best describes the effects on the capacitance?

A digital camera uses a capacitor system for its flash. Two capacitors, $$C_{1}=2.0\times10^{-6}\,\mathrm{F}$$ and $$C_{2}=3.0\times10^{-6}\,\mathrm{F}$$ , are connected in series to a $$100\,\mathrm{V}$$ battery. $$C_{1}$$ has $$41.50\,\mathrm{V}$$ while $$C_{2}$$ has $$27.67\,\mathrm{V}$$ . Which statement correctly explains why one capacitor has a larger voltage than the other in this series connection based on the relationship between capacitance, charge, and voltage?

Two point charges lie on the x-axis:

Q1 = +4.0 μC at x = 0.00 m;

Q2 = +3.0 μC at x = 0.40 m;

a test point P is at x = 0.20 m.

Which method correctly finds the net electric field at P?

You are designing a solar panel that acts like a flat sheet in a uniform vertical electric field E = 100 N/C. The panel can tilt to maximize or minimize the flux. Which orientation would maximize the electric flux, and how would you calculate it?

The electric potential in a region is $$V(x) = 3x^2 - 6x$$ . A student wants to place a charged particle at a point where it experiences no electric force. Which electric field expression and position should the student construct and choose to satisfy this condition?

A camera flash circuit must store about 20 μF of capacitance. You are given three capacitors with values 10 μF, 10 μF, and 12 μF. You may connect them in parallel only; not all capacitors must be used. Which design choice best meets the circuit requirement without exceeding 22 μF?

A camera flash circuit must store about 20 μF of capacitance. You are given three capacitors with values 10 μF, 10 μF, and 12 μF. You may connect them in parallel only, but not all capacitors must be used., what will you do to make the camera store more energy?

Two regions have different electric field strengths. Which conclusion is most reasonable?

Two students rub different objects: a plastic comb with hair and a glass rod with silk. Both become charged. Which conclusion best explains this?

Equipotential lines around a metal sphere are concentric circles, closest near the sphere. What is the direction of the electric field?

A metal object has equipotential lines very close near a sharp tip and widely spaced elsewhere. What can you infer about the electric field?

Between two nearby plates, equipotential lines are evenly spaced at $$100\ \mathrm{V}$$ , $$90\ \mathrm{V}$$ , $$80\ \mathrm{V}$$ … decreasing toward one plate. What best describes the electric field?

Who correctly calculated the work done by the field?