A charge particle having charge 4 × 10−3 C moves from state of rest in uniform electric field of magnitude 5 × 103 V/m. What is its KE after 10 second? (m = 2 × 10−9 kg)
Answers
Answer:
Notes and Solved Problems for Common Exam 1
1. ELECTRIC CHARGE
Key concepts:
Charged particles attract or repel each other. If particles have charges of the same sign
they repel each other. If their charges are of the opposite sign they attract each other.
Units of charge: Coulombs.
Coulomb’s Law states that the value of the force between two charged particles Q1 and
Q2 is proportional to their charges and is inversely proportional to the square of the
distance r between them:
1 2
2
Q Q F k
r
=
where coefficient 9 2 2 k Nm C = × 8.99 10 / which is sometimes expressed via another
constant
12 2 2
0
1
8.85 10 /
4
C Nm
k
ε
π
−
= = ×
Concept of charge density: for charge Q uniformly distributed over some volume V, the
charge per unit volume or volume charge density is the ratio ρ = Q V/
. If an object is
flat (2 dimensional) the surface charge density is the ratio of the charge Q to the surface
area S: σ = Q S/
. For linear, or 1 dimensional objects, the linear charge density is the
charge per unit length: λ = Q L/
. We therefore have:
3 : /
2 : /
1 : /
D Q V
D Q S
D Q L
ρ
σ
λ
=
=
=
These formulas define a uniform distribution.
Typical problems related to electric charge:
Problem 1. Two electrons are placed at a certain distance between each other? The force
between them is:
A. Repulsion
B. Attraction
C. Zero
D. Not determined
E. None of the above
Solution.
Two electrons have negative charge, therefore the force is repulsion. Answer A
Problem 2. Find force between a proton and an electron placed at the distance 1 µm.
A. 2.3 * 10-13N, attraction
B. 2.3 * 10-13N, repulsion
C. 2.3 * 10-16N, attraction
D. 2.3 * 10-16N, repulsion
E. 2.3 * 10-9N, attraction
Solution.
The force between two oppositely charged particles is attraction and its value is
19 19
1 2 9 16
2 6 2
1.6 10 1.6 10 8.99 10 2.3 10
(10 )
q q F k
r
− −
−
−
× × ×
= = × = ×
Answer C.
Problem 3. A postively charged particle with Q= 5 mC is placed between two negatively
charged particles with q1= 1 mC (left) and q2=9 mC (right). The distance between q1 and
q is 5 cm and the distance from q to q2 is 9 cm. What is the total force acting on the
middle particle? Find the value and the direction.
A) 3.2 x 107
N, left
B) 3.2 x 107
N, right
C) 2.8 x10-9 N, left
D) 2.8 x 10-9 N, right
E) Zero
Solution.
The value of the force from particle 1 on the middle particle is
3 3
1 9 7
1 2 2 2
1
1 10 5 10 8.99 10 1.8 10
(5 10 )
q Q F k
r
− −
−
× × ×
= = × = ×
×
The direction of this force is to the left since particle 1 and the middle particle are
oppositely charged and attract each other.
The value of the force from particle 2 on the middle particle is
3 3
2 9 7
2 2 2 2
B) East