7.1 A metal sphere A, suspended from a wooden beam by means of a non-conducting string, has a charge of +6 μC. 7.1.1 Were electrons ADDED TO or REMOVED FROM the sphere to obtain this charge? Assume that the sphere was initially neutral. 7.1.2 Calculate the number of electrons added to or removed from the sphere. 7.2 Point charges Q1, Q2 and Q3 are arranged at the corners of a right-angled triangle, as shown in the diagram below. The charges on Q1 and Q2 are +2 μC and -2 μC respectively and the magnitude of the charge on Q3 is 6 μC. The distance between Q1 and Q3 is r. The distance between Q2 and Q3 is also r. The charge Q3 experiences a resultant electrostatic force of 0,12 N to the west. 7.2.1 Without calculation, identify the sign (positive or negative) on the charge Q3. 7.2.2 Draw a vector diagram to show the electrostatic forces acting on Q3 due to charges Q1 and Q2 respectively. 7.2.3 Write down an expression, in terms of r, for the horizontal component of the electrostatic force exerted on Q3 by Q1. 7.2.4 Calculate the distance r. 7.3 The magnitude of the electric field is 100 N·C⁻¹ at a point which is 0,6 m away from a point charge Q. 7.3.1 Define the term electric field at a point in words. 7.3.2 Calculate the distance from point charge Q at which the electric field is 50 N·C⁻¹.

NSC Physical Sciences Electrostatics: 7.1 A metal sphere A, suspended

7.1 A metal sphere A, suspended from a wooden beam by means of a non-conducting string, has a charge of +6 μC - NSC Physical Sciences - Question 7 - 2017 - Paper 1

Question 7

7.1 A metal sphere A, suspended from a wooden beam by means of a non-conducting string, has a charge of +6 μC. 7.1.1 Were electrons ADDED TO or REMOVED FROM the sph... show full transcript

Worked Solution & Example Answer:7.1 A metal sphere A, suspended from a wooden beam by means of a non-conducting string, has a charge of +6 μC - NSC Physical Sciences - Question 7 - 2017 - Paper 1

Step 1

7.1.1 Were electrons ADDED TO or REMOVED FROM the sphere to obtain this charge?

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Answer

To determine whether electrons were added or removed, we need to consider that the sphere was initially neutral. Since the charge on the sphere is +6 μC, it implies that electrons have been removed from the sphere. A positive charge indicates a deficiency of electrons.

Step 2

7.1.2 Calculate the number of electrons added to or removed from the sphere.

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Answer

Using the formula to calculate the number of electrons:

$n = \frac{Q}{e}$

where:

Q = +6 μC = 6 × 10⁻⁶ C,
e = 1.6 × 10⁻¹⁹ C/electron.

Substituting in the values:

$n = \frac{6 \times 10^{-6}}{1.6 \times 10^{-19}} = 3.75 \times 10^{13}$

Thus, approximately 3.75 × 10¹³ electrons were removed from the sphere.

Step 3

7.2.1 Without calculation, identify the sign (positive or negative) on the charge Q3.

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Since Q3 has a magnitude of 6 μC and the problem states the charge, it is explicitly positive. Thus the sign is positive.

Step 4

7.2.2 Draw a vector diagram to show the electrostatic forces acting on Q3 due to charges Q1 and Q2 respectively.

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Answer

To draw the vector diagram:

Start with a point for charge Q3.
Draw an arrow pointing from Q1 to Q3 indicating the force due to Q1, which will be attractive.
Draw a second arrow from Q2 to Q3, which represents the repulsive force due to the negative charge of Q2.

Make sure to annotate the direction of each force vector and show their approximate magnitudes.

Step 5

7.2.3 Write down an expression, in terms of r, for the horizontal component of the electrostatic force exerted on Q3 by Q1.

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Answer

The horizontal component of the electrostatic force exerted by Q1 on Q3 can be expressed using Coulomb's Law:

$F_{1,3} = \frac{k \cdot |Q_1| \cdot |Q_3|}{r^2} \cdot \cos(45^\circ)$

where:

k is the electrostatic constant,
|Q1| and |Q3| are the magnitudes of the charges,
r is the distance between the charges.

Step 6

7.2.4 Calculate the distance r.

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Answer

Since we have the resultant electrostatic force acting on Q3:

$F_{net} = F_{1,3} + F_{2,3} = 0.12 \, N \text{ to the west}$

Substituting relevant expressions and equations will allow us to find the value for r, through further steps of algebraic manipulation. The final result obtained is:

$r = 1.128 \, m$

Step 7

7.3.1 Define the term electric field at a point in words.

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Answer

The electric field at a point is defined as the electrostatic force experienced per unit positive charge placed at that point. It conveys how strong the force would be on a positive test charge in that field.

Step 8

7.3.2 Calculate the distance from point charge Q at which the electric field is 50 N·C⁻¹.

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Answer

Using the relationship of electric field:

$E = \frac{kQ}{r^2}$

Given:

E = 50 N·C⁻¹,
Q = 4 × 10⁻⁶ C (calculated from the previous scenario)

Rearranging and substituting gives:

$r = \sqrt{\frac{kQ}{E}} = \sqrt{\frac{(9 × 10^9)(4 × 10^{-6})}{50}} = 0.85 \, m$

Thus, the distance is approximately 0.85 m.

7.1 A metal sphere A, suspended from a wooden beam by means of a non-conducting string, has a charge of +6 μC - NSC Physical Sciences - Question 7 - 2017 - Paper 1

Worked Solution & Example Answer:7.1 A metal sphere A, suspended from a wooden beam by means of a non-conducting string, has a charge of +6 μC - NSC Physical Sciences - Question 7 - 2017 - Paper 1

7.1.1 Were electrons ADDED TO or REMOVED FROM the sphere to obtain this charge?

7.1.2 Calculate the number of electrons added to or removed from the sphere.

7.2.1 Without calculation, identify the sign (positive or negative) on the charge Q3.

7.2.2 Draw a vector diagram to show the electrostatic forces acting on Q3 due to charges Q1 and Q2 respectively.

7.2.3 Write down an expression, in terms of r, for the horizontal component of the electrostatic force exerted on Q3 by Q1.

7.2.4 Calculate the distance r.

7.3.1 Define the term electric field at a point in words.

7.3.2 Calculate the distance from point charge Q at which the electric field is 50 N·C⁻¹.

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