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SECTION 2.2 (35 points) Three charges are arranged in a line as shown. While their signs are different, they each have a magnitude of 1 nC and a mass of 10-10 kg. Also d 2 cm and d2 1 41 42 a. Which of the four regions: left ofqh, between q,and q2, between q2 and qs, and right of q3 contains a finite point at which the electric potential zero? b. How much electric potential energy is stored in this configuration? c. If the negative charge were replaced by an equivalent but positive charge and the three were released to move freely, how fast would q, end up moving? Solution part A : Since q2 and q3 are of opposite charges, field lines between them wil be repeling so Electric potential between them can be zero as potential is a scalar ------------------ ELectric Potential energy Unet = U12 + U23 + U13 Unet = Kq1q2/d1 + Kq2q3/d2 + Kq1q3/(d1+d2) Unet = 9*10^9 * 1*10^-9*1*10^-9*(1/0.02 - 1/0.01 - 1/0.03) Unet = -7.5*10^-7 JOules --------------------------- part C: for +ve charge net Energy Unet = Kq1q2/d1 + Kq2q3/d2 + Kq1q3/(d1+d2) Unet = 9*10^9 * 1*10^-9*1*10^-9*(1/0.02 + 1/0.01 + 1/0.03) Unet = 1.65 *10^-6 but ENergy = 0.5 mv^2 v^2 = 2 Une/m v^2 = 2 * 1.65 *10^-6/(10^-10) V = 3.3 *10^4 m/s .

SECTION 2.2 (35 points) Three charges are arranged in a line as shown. While their signs are
different, they each have a magnitude of 1 nC and a mass of 10-10 kg. Also d 2 cm and d2 1 41
42 a. Which of the four regions: left ofqh, between q,and q2, between q2 and qs, and right of q3
contains a finite point at which the electric potential zero? b. How much electric potential energy
is stored in this configuration? c. If the negative charge were replaced by an equivalent but
positive charge and the three were released to move freely, how fast would q, end up moving?
Solution
part A :
Since q2 and q3 are of opposite charges, field lines between them wil be repeling
so Electric potential between them can be zero as potential is a scalar
------------------
ELectric Potential energy Unet = U12 + U23 + U13
Unet = Kq1q2/d1 + Kq2q3/d2 + Kq1q3/(d1+d2)
Unet = 9*10^9 * 1*10^-9*1*10^-9*(1/0.02 - 1/0.01 - 1/0.03)
Unet = -7.5*10^-7 JOules
---------------------------
part C:
for +ve charge
net Energy Unet = Kq1q2/d1 + Kq2q3/d2 + Kq1q3/(d1+d2)
Unet = 9*10^9 * 1*10^-9*1*10^-9*(1/0.02 + 1/0.01 + 1/0.03)
Unet = 1.65 *10^-6

but ENergy = 0.5 mv^2
v^2 = 2 Une/m
v^2 = 2 * 1.65 *10^-6/(10^-10)
V = 3.3 *10^4 m/s

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1. SECTION 2.2 (35 points) Three charges are arranged in a line as shown. While their signs are different, they each have a magnitude of 1 nC and a mass of 10-10 kg. Also d 2 cm and d2 1 41 42 a. Which of the four regions: left ofqh, between q,and q2, between q2 and qs, and right of q3 contains a finite point at which the electric potential zero? b. How much electric potential energy is stored in this configuration? c. If the negative charge were replaced by an equivalent but positive charge and the three were released to move freely, how fast would q, end up moving? Solution part A : Since q2 and q3 are of opposite charges, field lines between them wil be repeling so Electric potential between them can be zero as potential is a scalar ------------------ ELectric Potential energy Unet = U12 + U23 + U13 Unet = Kq1q2/d1 + Kq2q3/d2 + Kq1q3/(d1+d2) Unet = 9*10^9 * 1*10^-9*1*10^-9*(1/0.02 - 1/0.01 - 1/0.03) Unet = -7.5*10^-7 JOules --------------------------- part C: for +ve charge net Energy Unet = Kq1q2/d1 + Kq2q3/d2 + Kq1q3/(d1+d2) Unet = 9*10^9 * 1*10^-9*1*10^-9*(1/0.02 + 1/0.01 + 1/0.03) Unet = 1.65 *10^-6

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