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A small metal sphere Y carries a charge of + 6 x 10⁶ C - NSC Physical Sciences - Question 8 - 2018 - Paper 1
Question 8
A small metal sphere Y carries a charge of + 6 x 10⁶ C. 8.1 Draw the electric field pattern associated with sphere Y. 8.2 If 8 x 10¹³ electrons are now transferred... show full transcript
Worked Solution & Example Answer:A small metal sphere Y carries a charge of + 6 x 10⁶ C - NSC Physical Sciences - Question 8 - 2018 - Paper 1
Step 1
8.1 Draw the electric field pattern associated with sphere Y.
Answer
To represent the electric field pattern associated with sphere Y:
- Draw a small circle to represent the metal sphere Y.
- From the sphere, draw several straight lines radiating outward. These lines should point away from the sphere, indicating that it has a positive charge.
- Ensure that the lines do not cross each other and are evenly spaced, symbolizing the uniform nature of the electric field around a charged sphere.
Step 2
8.2 If 8 x 10¹³ electrons are now transferred to sphere Y, calculate the electric field at a point 0.5 m from the sphere.
Answer
First, calculate the charge of the transferred electrons:
egin{align*} Q &= n imes e \ &= (8 imes 10^{13}) imes (1.6 imes 10^{-19}) \ &= -12.8 imes 10^{-6} ext{ C} \ \end{align*}
Next, find the net charge on sphere Y:
egin{align*} Q_{net} &= (6.0 imes 10^{-6}) + (-12.8 imes 10^{-6}) \ &= -6.8 imes 10^{-6} ext{ C} \ \end{align*}
To calculate the electric field (E) at a point 0.5 m from the sphere:
egin{align*} E &= \frac{kQ}{r^2} \ &= \frac{(9 imes 10^9)(-6.8 imes 10^{-6})}{(0.5)^2} \ &= -2.45 imes 10^5 ext{ N C}^{-1} \text{ towards sphere Y} \ \end{align*}
This indicates that the electric field points towards the sphere, consistent with the negative charge.