exam1_08

# exam1_08 - Exam No 1 Solutions I(20 pts Three positive...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Exam No. 1 Solutions I. (20 pts) Three positive charges q 1 = +2 μ C, q 2 = +1 μ C, and q 3 = +1 μ C are arranged at the corners of an equilateral triangle of side 2 m as shown in the diagram. Calculate: a) The force exerted on q 1 by the other charges. Answer: Because charges q 2 and q 3 are equal, and q 1 lies on the line bisecting the two charges, the horizontal components will cancel, leaving only ti o p r the ver cal c m onents, o ܧ ሬ ௬ ሺݍ ଶ ሻ ൌ ܧ ሬ ௬ ሺݍ ଷ ሻ ൌ ݍ 4ߨ߳ ଴ ݎ ଶ cos ߠ ൌ ሺ9 x 10 ଽ Nm ଶ C ିଶ ሻሺ1 x 10 ି଺ Cሻ ଶ ሺ2mሻ cos 30 ° ൌ ሺ1.95 x 10 NC ሻ ܨ ൌ ݍ ଵ · ቀܧ ሬ ଷ ିଵ ௬ ሺݍ ଶ ሻ ൅ ܧ ሬ ௬ ሺݍ ଷ ሻ ି଺ C 2 · ሺ1.95 x 10 ଷ NC ିଵ ሻ ቁ ൌ ሺ2 x 10 ሻ · ൌ ૠ. ૡ ܠ ૚૙ ି૜ ۼ b) The electrostatic potential energy of the system of charges Answer: There are a number of ways to describe the potential energy associated with assembling a system of charges, ܷ ൌ 1 4ߨ߳ ଴ ෍ ݍ ௜ ݍ ௝ ݎ ௜௝ ௜ழ௝ ൌ 1 2 ෍ ݍ ௜ ݍ ௝ 4ߨ߳ ଴ ݎ ௜௝ ௜,௝,௜ஷ௝ ൌ 1 2 ෍ ݍ ௜ ܸ ௜ ௜ where V i is the potential at q i due to all the other charges, but the answers will all be the same. 1 For this assembly, ܷ ൌ 1 4ߨ߳ ଴ ݍ ଵ ݍ ଶ ݎ ଵଶ ൅ 1 4ߨ߳ ଴ ݍ ଵ ݍ ଷ ݎ ଵଷ ൅ 1 4ߨ߳ ଴ ݍ ଶ ݍ ଷ ݎ ଶଷ Since ݎ ଵଶ ൌ ݎ ଵଷ ൌ ݎ ଶଷ , this becomes ܷ ൌ 1 4ߨ߳ ଴ ݎ ൌ ݎ ሺݍ ଵ ݍ ଶ ൅ ݍ ଵ ݍ ଷ ൅ ݍ ଶ ݍ ଷ ሻ m C ିଶ ሻ ൌ ሺ9 x 10 ଽ N ଶ 2 ቀ2൫ሺ2 x 10 ି଺ Cሻሺ1 x 10 ି଺ Cሻ൯ ൅ ሺ1 x 10 ି଺ Cሻሺ1 x 10 ି଺ Cሻቁ ൌ ૛. ૛૞ ܠ ૚૙ ି૛ ۸ c) A charge is now placed midway between q 2 and q 3 at point A. If the object is released from rest at this point, what is its velocity when it is a large distance from the three charges? (Take ଵ ସగఌ బ ൌ 9 x 10 ଽ ) Answer: This portion of the question requires recognizing that, far from the surface, the potential energy of a particle initially placed at position A will all be converted to kinetic energy, and the question is asking to solve for the velocity associated with that kinetic energy. The potential energy, U , that th ar wil av at A ill e U q 4 V , where V is the potential at A produced by th , the 4 ch ge l h e w b = e three positive charges, q 1 q 2 and q 3 . ସ q ଵ ܷ ൌ ݍ ൬ 4ߨ߳ ଴ ݎ ଵ ൅ ଶ 4ߨ߳ ଴ ݎ ଶ q ൅ q ଷ 4ߨ߳ ଴ ݎ ଷ ൰ ൌ ሺ3 x 10 ି଺ Cሻሺ9 x 10 ଽ Nm ଶ C ିଶ ሻ ቆ ሺ2 x 10 ି଺ Cሻ 3 2m cos 0° ൅ ሺ1 x 10 ି଺ Cሻ 1m ൅ ሺ1 x 10 ି଺ Cሻ 1m ቇ ൌ ૡ. ૞ ܠ ૚૙ ି૛ ۼܕ The loss of this potential energy will result in a gain in kinetic energy, so that far from the...
View Full Document

{[ snackBarMessage ]}

### Page1 / 10

exam1_08 - Exam No 1 Solutions I(20 pts Three positive...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online