Question

A −12 nC-12\,	ext{nC} charge is located at (x,y)=(1.0 cm,0 cm)(x, y)=(1.0\,	ext{cm}, 0\,	ext{cm}). What are the electric fields at the positions (x,y)=(5.0 cm,0 cm),(−5.0 cm,0 cm)(x,y)=(5.0\,	ext{cm},0\,	ext{cm}),(-5.0\,	ext{cm},0\,	ext{cm)}, and (0 cm,5.0 cm)(0\,	ext{cm}, 5.0\,	ext{cm})? Write each electric field vector in component form.

Accepted Answer

Step 1: Recall the formula for the electric field due to a point charge: E = k_e * |q| / $$r^2$$, where k_e is Coulomb's constant ($$8.99 × 10^9$$ \, N·$$m^2$/C^2$$), q is the charge, and r is the distance between the charge and the point where the field is being calculated. Step 2: Convert all distances to meters. The charge is located at (1.0 cm, 0 cm), which is (0.01 m, 0 m). The positions where the electric field is to be calculated are (5.0 cm, 0 cm) = (0.05 m, 0 m), (−5.0 cm, 0 cm) = (−0.05 m, 0 m), and (0 cm, 5.0 cm) = (0 m, 0.05 m). Step 3: Calculate the distance r between the charge and each point. For example, for (5.0 cm, 0 cm), r = |$$x_2$$ - $$x_1$$|, where $$x_1 = 0.01$$ \, m and $$x_2 = 0.05$$ \, m. Repeat this for the other two points. Step 4: Determine the direction of the electric field. The electric field vector points away from the charge if it is positive and toward the charge if it is negative. Since the charge is -12 \, nC, the electric field vectors will point toward the charge. Use the relative positions of the charge and the points to determine the components of the electric field vector. Step 5: Substitute the values of k_e, q, and r into the formula for the electric field. For each point, calculate the magnitude of the electric field and then resolve it into components based on the direction determined in Step 4. Write the electric field vectors in component form for each position.

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Key Concepts

Electric Field

Coulomb's Law

Vector Components