QCE Vault / Physics Electromagnetism — Question 257 Original QCE Vault practice · 1 mark
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QUESTION 257 Two small identical spheres carry equal positive charges q q q . Their centres are 0.200 m 0.200\,\mathrm m 0.200 m apart and they repel with force 0.0900 N 0.0900\,\mathrm N 0.0900 N . Use k = 9.00 × 10 9 N m 2 C − 2 k=9.00\times10^9\,\mathrm{N\,m^2\,C^{-2}} k = 9.00 × 1 0 9 N m 2 C − 2 . What is q q q ? (A) 4.00 × 10 − 13 C 4.00\times10^{-13}\,\mathrm C 4.00 × 1 0 − 13 C (B) 4.00 × 10 − 7 C 4.00\times10^{-7}\,\mathrm C 4.00 × 1 0 − 7 C (C) 6.32 × 10 − 7 C 6.32\times10^{-7}\,\mathrm C 6.32 × 1 0 − 7 C (D) 2.00 × 10 − 6 C 2.00\times10^{-6}\,\mathrm C 2.00 × 1 0 − 6 C WORKED SOLUTION
Answer C 1 mark ANSWER C. 6.32 × 10 − 7 C 6.32\times10^{-7}\,\mathrm C 6.32 × 1 0 − 7 C Worked solution
F = k q 2 / r 2 F=kq^2/r^2 F = k q 2 / r 2 , so q = F r 2 / k = 0.0900 ( 0.200 ) 2 / ( 9.00 × 10 9 ) = 6.32 × 10 − 7 C q=\sqrt{Fr^2/k}=\sqrt{0.0900(0.200)^2/(9.00\times10^9)}=6.32\times10^{-7}\,\mathrm C q = F r 2 / k = 0.0900 ( 0.200 ) 2 / ( 9.00 × 1 0 9 ) = 6.32 × 1 0 − 7 C . Taking a square root is essential because both charges are unknown and equal. Equivalent physically justified methods, alternative valid sketches and consistent units accepted.
Accept sensible significant figures and consistent rounding from stated constants.
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