A wall has a negative charge distribution producing a uniform horizontal electric field.
A small plastic ball of mass 0.0261 kg, carrying charge of −102 μC, is suspended by an uncharged, nonconducting thread 0.369 m
long. The thread is attached to the wall and the ball hangs in equilibrium in the electric and gravitational fields.
Find the magnitude of the electric field at the ball’s location due to the charged wall. Assume the electric force on the ball has a magnitude of 0.0363 N. The acceleration due
to gravity is 9.8 m/s2 .
Answer in units of N/C
20N
To find the magnitude of the electric field at the ball's location due to the charged wall, we can use the equation for electric force:
Electric Force = Electric Field * Charge
Given that the electric force on the ball has a magnitude of 0.0363 N and the charge of the ball is -102 μC, we can substitute these values into the equation to solve for the electric field:
0.0363 N = Electric Field * (-102 μC)
First, let's convert the charge from μC to C:
-102 μC = -102 * 10^(-6) C
Now we can substitute this value into the equation:
0.0363 N = Electric Field * (-102 * 10^(-6) C)
Next, we need to solve for the Electric Field. We can rearrange the equation to isolate the Electric Field:
Electric Field = 0.0363 N / (-102 * 10^(-6) C)
Now, let's calculate this value:
Electric Field = 0.0363 N / (-102 * 10^(-6) C)
Electric Field = -0.0363 N / 102 * 10^(-6) C
Electric Field = -0.0363 / 102 * 10^(-6) N/C
Electric Field = -3.5588 * 10^(-4) N/C
So, the magnitude of the electric field at the ball's location, due to the charged wall, is approximately 3.5588 * 10^(-4) N/C.