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Kinematic equations with a charge

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Wize University Physics Textbook (Master) > Newton's Laws of Motion: Forces and Dynamics

Electrostatic Force

3 Activities

An electron is shot at an initial speed of 3.00 × 106 m/s, perpendicular to a uniform electric field, as shown below. Electrons hits the right plate at vertical distance 6.00 cm.
a) If the electron was 4.00 cm away from this plate initially, calculate the magnitude of the electric field.
b) What is the direction?
(Note: the video mistakenly uses 3.00 x 105 m/s as the initial velocity, but all of the calculations use 3.00 x 106 m/s!)
a) Magnitude (enter in units of 103 N/C)
More Electrostatic Force Questions:
Conductors, Insulators and Induced Charges
Practice: Conductors, Insulators, and Induced Charge
Consider two spheres; they are either positively charged, negatively charged, or neutral.
a) What can you say about the charge on the two spheres if they are electrically attracted to each other?
Coulomb’s Law
Two point charges are located on the x-axis as shown below.
a) Where should a third charge, q3=+8.00μCq_3=+8.00\mu C, be placed on the y-axis so that the net force on q2q_2 makes an angle of +45°+45\degree above the negative x-axis?
b) For additional practice: What is the magnitude of the net force? (Not in video; see written solution)
Square of charges
Four charges are arranged in a square with sides of length 2.5 cm.
Find the net force on q1 (both magnitude and direction)
Kinematic equations with a charge
An electron is shot at an initial speed of 3.00 × 106 m/s, perpendicular to a uniform electric field, as shown below. Electrons hits the right plate at vertical distance 6.00 cm.
a) If the electron was 4.00 cm away from this plate initially, calculate the magnitude of the electric field.
b) What is the direction?
Coulomb’s Law
EX: Two point charges are located on the x-axis as shown below.
a) Where should a third charge, q3=+8.00μCq_3=+8.00\mu C, be placed on the y-axis so that the net force on q2q_2 makes an angle of +45°+45\degree above the negative x-axis?
b) For additional practice: What is the magnitude of the net force? (Not in video; see written solution)
Placing a third charge - x-axis
EX: Two point charges are located as shown below.
a) Where should be a third negative chargeq3q_3be placed on the x-axis such that the net forces onq1q_1 andq2q_2 be equal to zero?
b) What should the magnitude of the charge be?
Conductors, Insulators and Induced Charges
Practice: Conductors, Insulators, and Induced Charge
Consider two spheres; they are either positively charged, negatively charged, or neutral.
a) What can you say about the charge on the two spheres if they are electrically attracted to each other?
Placing a third charge - x-axis
Two point charges are located as shown below.
a) Where should be a third negative charge q3q_3 be placed on the x-axis such that the net forces on q1q_1 and q2q_2 be equal to zero?
b) What should the magnitude and sign of the charge be?
Coulomb’s Law
Two point charges are located on the x-axis as shown below.
a) Where should a third charge, q3=+8.00μCq_3=+8.00\mu C, be placed on the y-axis so that the net force on q2q_2 makes an angle of +45°+45\degree above the negative x-axis?
b) For additional practice: What is the magnitude of the net force? (Not in video; see written solution)
Square of charges
Four charges are arranged in a square with sides of length 2.5 cm.
Find the net force on q1 (both magnitude and direction)
Placing a third charge - y-axis
Practice: Coulomb's Law with Vectors
Two point charges are located on the x-axis as shown below.
a) Where should a third charge, q3=+8.00μCq_3=+8.00\mu C, be placed on the y-axis so that the net force on q2q_2 makes an angle of +45°+45\degree above the negative x-axis?
Conductors, Insulators and Induced Charges
Practice: Conductors, Insulators, and Induced Charge
Consider two spheres; they are either positively charged, negatively charged, or neutral.
a) What can you say about the charge on the two spheres if they are electrically attracted to each other?
Kinematic equations with a charged particle
Practice: Electron Moving Between Two Plates
An electron is shot at an initial speed of 3.00 × 106 m/s up the page. There is a uniform electric field that points from one parallel plate to the other, and the electron starts moving towards the plate on the right, as shown below. The electron hits the right plate at vertical distance of 6.00 cm above where it started.
a) Based on the direction of the electron motion shown below, what is the direction of the electric field?
Kinematic equations with a charged particle
Practice: Electron Moving Between Two Plates
An electron is shot at an initial speed of 3.00 × 106 m/s up the page. There is a uniform electric field that points from one parallel plate to the other, and the electron starts moving towards the plate on the right, as shown below. The electron hits the right plate at vertical distance of 6.00 cm above where it started.
a) Based on the direction of the electron motion shown below, what is the direction of the electric field?
Placing a third charge - y-axis
Practice: Coulomb's Law with Vectors
Two point charges are located on the x-axis as shown below.
a) Where should a third charge, q3=+8.00μCq_3=+8.00\mu C, be placed on the y-axis so that the net force on q2q_2 makes an angle of +45°+45\degree above the negative x-axis?
Square of charges
Four charges are arranged in a square with sides of length 2.5 cm.
Find the net force on q1 (both magnitude and direction).
...........
Conductors, Insulators and Induced Charges
Example: Conductors, Insulators, and Induced Charge
Consider two spheres; they are either positively charged, negatively charged, or neutral.
a) What can you say about the charge on the two spheres if they are electrically attracted to each other?
An electron (me = 9.109 x 10-31 kg) travels due north at a speed of 2.0 x 105 m/s. A constant electric field stops the electron in a distance of 10m. What is its magnitude and orientation?
At a certain point on Earth, there is a constant electric field E pointing downwards. A small ball of negligible mass carrying a charge of q is thrown straight upwards with a velocity v0. How high does the ball get if: a) q is positive? b) q is negative?
An ion with charge of 3.2 x 10-19 C and mass of 6.64 x 10-27 kg starts in a region with E=500 N/C k^\hat k . It moves for Δz=3m k^\Delta z=3m\,\hat k and then experiences a constant magnetic field.
With what speed does it enter the magnetic field region?
What magnetic field is required so that the ion continues with a constant velocity?
Placing a third charge - x-axis
Two point charges are located as shown below.
a) Where should be a third negative chargeq3q_3be placed on the x-axis such that the net forces onq1q_1 andq2q_2 be equal to zero?
b) What should the magnitude of the charge be?
Square of charges
Four charges are arranged in a square with sides of length 2.5 cm.
Find the net force on q1 (both magnitude and direction)
Coulomb’s Law
Two point charges are located on the x-axis as shown below.
a) Where should a third charge, q3=+8.00μCq_3=+8.00\mu C, be placed on the y-axis so that the net force on q2q_2 makes an angle of +45°+45\degree above the negative x-axis?
b) For additional practice: What is the magnitude of the net force? (Not in video; see written solution)
Conductors, Insulators and Induced Charges
Consider two spheres; they are either positively charged, negatively charged, or neutral.
a) What can you say about the charge on the two spheres if they are electrically attracted to each other?
(NB: In the video, I give one possible case - what are the other possible cases? See written solution!)