Consider three charges arranged as shown.
The picture is three particles in a horizontal line. There charges are represented below in order
A B C
+ + −
the distance from A to B is 4.4 cm. The distance from B to C is 4.6 cm
A=8.2 µC B=4.5 µC C=−4 µC
What is the magnitude of the electric field strength at a point 1.5 cm to the left of the middle charge? The value of the Coulomb constant is 8.98755×10^9N�m2/C2.
Answer in units of N/C
What is the magnitude of the force on a −4 µC charge placed at this point?
Answer in units of N
I know we use F=KQ1Q2/r^2
I tried to set up 3 different forces and then add them together... I did not get it right.
Please help!
To find the magnitude of the electric field strength at a point 1.5 cm to the left of the middle charge, we need to consider the contributions of all three charges to the electric field at that point. Let's break it down step by step.
First, let's calculate the electric field strength due to the charge at point A. The formula for electric field strength is given by:
E = k * Q / r²
where E is the electric field strength, k is the Coulomb constant (8.98755×10^9 N m^2/C^2), Q is the charge, and r is the distance between the charge and the point where we want to find the electric field.
For charge A:
QA = 8.2 µC
RA = 1.5 cm (distance between A and the desired point)
Convert µC to C:
QA = 8.2 × 10^-6 C
Convert cm to m:
RA = 1.5 × 10^-2 m
Now, let's calculate the electric field strength due to charge B and charge C using the same process.
For charge B:
QB = 4.5 µC
RB = 4.4 cm (distance between B and the desired point)
Convert µC to C:
QB = 4.5 × 10^-6 C
Convert cm to m:
RB = 4.4 × 10^-2 m
For charge C:
QC = -4 µC
RC = 4.6 cm (distance between C and the desired point)
Convert µC to C:
QC = -4 × 10^-6 C
Convert cm to m:
RC = 4.6 × 10^-2 m
Now, let's calculate the electric field strength due to each charge using the formula E = k * Q / r²:
EA = (8.98755×10^9 N m^2/C^2) * (8.2 × 10^-6 C) / (1.5 × 10^-2 m)²
EB = (8.98755×10^9 N m^2/C^2) * (4.5 × 10^-6 C) / (4.4 × 10^-2 m)²
EC = (8.98755×10^9 N m^2/C^2) * (-4 × 10^-6 C) / (4.6 × 10^-2 m)²
Now, to find the total electric field strength at the desired point, we need to sum up the contributions from all charges:
Total E = EA + EB + EC
Finally, to calculate the force on a -4 µC charge placed at this point, we use the formula:
F = q * E
where F is the force, q is the charge, and E is the electric field strength at the point.
F = (-4 × 10^-6 C) * Total E
By substituting the calculated values into the equations, you should be able to find the answers.
Please note that in your question, the charge of C is already given as negative, so there is no need to add another negative sign when calculating the electric field and force.