# Problem 1

```SP212
Worksheet 4
Ch 22.(6,7) Charges and Dipoles in an electric field
Problem 1
A disk of radius R has a uniform surface charge of σ = 5&micro;C/m2 smeared across it. A proton is
released from a point on the disk’s axis above the disc. What is the acceleration of the proton if it
is released from the following distances:
a) released from a distance z = R
b) released from a distance z = R/2
c) released from a distance z = 20R
proton has a mass of 1.67 &times; 10−27 kg and the same charge as an electron, 1.61 &times; 10−19 C.
HINT: The electric field due to a uniformly charged disk is E = 2σ0 1 − √z2z+R2 where k =
1
4π0
2
and 0 = 8.85 &times; 10−12 NCm2
This problem is relevant for HW L4 problem 48.
Problem 2
A charge of size −4&micro;C is placed at the origin of an xy coordinate system. Another charge of size
+4&micro;C is placed at the position x = 2 &times; 10−10 m and y = −4 &times; 10− 10 m.
a) In component form (i.e. using î and ĵ) what is the dipole moment of this two charge system?
What is the magnitude of the dipole moment?
~ = 5000î N/C. What is the potential energy of
b) This dipole is placed in a constant electric field E
the dipole? What is the torque (as a vector) acting on the dipole?
c) If I reached down ad rotated this dipole by 180◦ , how much work would I have to do on the dipole?
TIP: remember that the work done by a conservative force is given by W = −∆U
This problem is relevant for HW L4 problems 59 and 83.
```