Q1. Three charged particles are placed in a line. The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two.

Background

Topic: Coulomb's Law and Superposition Principle

This question tests your understanding of how to calculate the electric force between point charges using Coulomb's Law and how to use vector addition (superposition) to find the net force on each charge.

Key Terms and Formulas

• Coulomb's Law:

• (Coulomb's constant)

• Superposition Principle: The net force on a charge is the vector sum of the forces exerted by all other charges.

Step-by-Step Guidance

1. Label the charges as , , and , with $q_2$ in the center and $q_1$, $q_3$ on either side, each 0.35 m from $q_2$.

2. Calculate the force between and using Coulomb's Law. Remember to consider the direction (attractive or repulsive) based on the sign of the charges.

3. Calculate the force between and in the same way.

4. For the center charge (), add the forces from and as vectors (since they are along the same line, this is a 1D addition).

5. For the end charges ( and ), remember each experiences forces from both the center and the other end charge. Set up the equations for these forces, considering their directions.

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Q2. Three positive particles of equal charge are located at the corners of an equilateral triangle of side 15.0 cm. Calculate the magnitude and direction of the net force on each particle due to the other two.

Background

Topic: Coulomb's Law and Vector Addition in Two Dimensions

This question tests your ability to calculate the net electrostatic force on a charge due to two other charges arranged in a triangle, requiring vector addition at an angle.

Key Terms and Formulas

• Coulomb's Law:

  (since all charges are equal and positive)

• Vector Addition: Forces from each charge must be added as vectors, considering the 60° angle between them in an equilateral triangle.

Step-by-Step Guidance

1. Choose one charge to analyze (the symmetry means the result will be the same for each).

2. Calculate the magnitude of the force between this charge and one of the other charges using Coulomb's Law, with m.

3. Repeat for the force from the other charge (it will have the same magnitude).

4. Draw the two force vectors at a 60° angle to each other (since the triangle is equilateral).

5. Set up the vector addition (using components or the law of cosines) to find the net force's magnitude and direction. Do not compute the final value yet—write the setup for the resultant.

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Q3. Determine the magnitude and direction of the electric field at a point midway between a and a charge 6.0 cm apart. Assume no other charges are nearby.

Background

Topic: Electric Field Due to Point Charges

This question tests your ability to calculate the electric field at a point due to multiple point charges, using the principle of superposition.

Key Terms and Formulas

• Electric Field of a Point Charge:

• Superposition Principle: The net electric field is the vector sum of the fields from each charge.

Step-by-Step Guidance

1. Find the distance from each charge to the midpoint (half of 6.0 cm = 3.0 cm = 0.03 m).

2. Calculate the electric field at the midpoint due to the charge (direction: toward the negative charge).

3. Calculate the electric field at the midpoint due to the charge (direction: away from the positive charge).

4. Set up the net electric field as the algebraic sum of the two fields, considering their directions (they point in opposite directions).

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Q4. Two point-charges and are separated by a distance of 12 cm. The electric field at point P is zero. How far from is P?

Background

Topic: Electric Field Zero Point Between Two Charges

This question tests your understanding of where the electric field cancels between two charges of opposite sign and how to set up the equation for the zero field location.

Key Terms and Formulas

• Electric Field of a Point Charge:

• Set the sum of the fields from both charges equal to zero at point P.

Step-by-Step Guidance

1. Let the distance from to point P be , and from to P be meters.

2. Write the equation for the electric field at P due to both charges and set their sum to zero: .

3. Substitute the expressions for each field: and , with correct signs for direction.

4. Set up the equation and solve for (do not compute the final value yet).

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Q5. Use Coulomb’s law to determine the magnitude and direction of the electric field at points A and B in the figure below due to the two positive charges () shown. Draw the electric field vectors for each charge and the net electric field, at both points.

Background

Topic: Electric Field from Multiple Point Charges in 2D

This question tests your ability to calculate the electric field at specific points due to multiple charges, using vector addition in two dimensions.

Key Terms and Formulas

• Electric Field of a Point Charge:

• Decompose the electric field vectors into and components for vector addition.

Step-by-Step Guidance

1. Calculate the distance from each charge to points A and B using the Pythagorean theorem.

2. Find the electric field at A due to each charge, determining both magnitude and direction (use symmetry and geometry).

3. Break each field into and components.

4. Add the components from both charges to find the net electric field at A. Repeat for point B.

5. Draw the vectors for each field and the net field at both points (as requested).

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Q6. In the following figure, two objects, and have charges as shown, and a third object, is electrically neutral. a) What is the electric flux through the surface that encloses all three objects? b) What is the electric flux through the surface that encloses the third object only?

Background

Topic: Gauss's Law and Electric Flux

This question tests your understanding of electric flux and how to apply Gauss's Law to closed surfaces.

Key Terms and Formulas

• Gauss's Law:

• is the total charge enclosed by the surface.

Step-by-Step Guidance

1. For part (a), sum the charges inside (, , and ) to find .

2. Apply Gauss's Law to calculate the flux through .

3. For part (b), note that encloses only , which is neutral.

4. Apply Gauss's Law for using .

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Q7. A cube of side 8.50 cm is placed in a uniform field with edges parallel to the field lines. a) What is the net flux through the cube? b) What is the flux through each of its six faces?

Background

Topic: Electric Flux in Uniform Fields

This question tests your understanding of electric flux through a closed surface in a uniform electric field, especially when the field is parallel to the faces of the cube.

Key Terms and Formulas

• Electric Flux:

• For a closed surface in a uniform field, the net flux is zero if no charge is enclosed.

Step-by-Step Guidance

1. For part (a), recall that the net flux through a closed surface in a uniform field is zero if there is no charge inside.

2. For part (b), calculate the flux through one face: , where is the area of one face and is the angle between the field and the normal to the face.

3. Determine which faces have nonzero flux (those perpendicular to the field) and which have zero flux (those parallel to the field).

4. Set up the calculation for the flux through each face, but do not compute the final value yet.

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