Electric Fields - Physics- MCAT

I think I will tackle the question on electric fields, electric potential and work done in an electric field in parts. First, I will discuss electric fields.

What is an electric field? Imagine you have a positive point charge and place a test positive charge in its vicinity. Coulomb’s law tells us that there is repulsion between the two charges. How exactly do the two charges feel one another? Then answer is the positive point charge sets up an electric field in the space around it. At any point within the space, the electric field has both a magnitude and a direction. The magnitude is dependent on the value of the charge and direction depends on the electrical charge. The electric field is a vector field and is defined for each point in space. By definition, the electrostatic force a test charge qo will feel in the vicinity of a point charge is:

E = F/ qo

The unit for electric field is N/C.

How do we draw electric field lines? Electric field lines give us a representation of the electric field. Say we have a sphere of uniform negative electric charge. If a positive test charge were placed in the field, the test charge would feel an electrostatic force pointed toward the sphere. This tells us that for negative charges, electric field lines point in. What if we have a sphere of uniform positive electric charge? If a positive test charge were placed in the field, the test charge would feel an electrostatic force pointed away from the sphere. Therefore, for positive charges, electric field lines point outward. How do electric field lines relate to electric field vectors? Simple! The electric field vector is tangent to the electric field line. For straight field lines, this means the electric field is that direction!

What is the electric field due to a point charge? Instead of a uniform sphere of charge, suppose we have a point charge and place a test charge qo in the vicinity. How would we calculate the electric field? From above, we know E = F/ qo. F is the electrostatic force which is given by Kq qo/r2, where r is the distance between the charges. Using the equation above, we see this reduces to: Kq/r2. Now, for some important points:
1. The above equation gives us the value for the electric field for all points in space for a point charge
2. The electric field is a vector—VERY IMPORTANT!!!
3. If there is more than one point charge, the electric fields are additive.

What would happen if we were to place a test charge in an electric field produced by a moving charge? Well, the electrostatic force that the test charge would feel is given by:

F=qE

Where q is the electric charge of the particle, and E is the electric field produced by the moving charge. Examining this equation, we see that if a negative charge is placed in the electric field produced by a positive charge, there is a negative electrostatic force due to attraction (This attraction can be verified using Coulomb’s law). Therefore, the direction of the electrostatic force has the direction of the electric field if the test charge is positive and will have the opposite direction if the test charge is negative. This is important! If on the MCAT, you are given a diagram of a electric field and given a test charge, and are asked the direction of the electrostatic force, you can use the procedure outlined above. Given all this information, you can also calculate the acceleration of the test charge. If the only force acting on the test charge is the electrostatic force, than you can set that value equal to F=ma, where F is the sum of the net forces. This can all be related to Newton’s second law!!

Question: (imagine this was a MCAT question) What if you are given a diagram of a negative test charge in a electric field pointing outward and you asked to determine whether the acceleration would increase if the test charge were moving in the direction of the electric field? First, if the electric field is pointing outward, than the point charge is positive. From Coulomb’s law, we know there is attraction between the test charge and point charge. Therefore, the electrostatic force, the net force, should be pointing inward. However, the test charge is moving away from the point charge. Since the electric field decreases with distance (Kq/r2), this means if qE=ma, than the acceleration will decrease. That’s it! On the MCAT, you would circle the answer choice with decreases!

Now, for a real world application of electric fields and charge. Believe it or not, you can use this analysis for ink-jet printers. You don’t need to know this for the MCAT!!!

In the printer, when the print command is received, a generator generates drops. These drops then pass through a charge unit and receive a charge q. These drops then pass through a pair of conducting plates where the electric field points down from the top plate to the bottom plate. Once these drops pass through the plates, they are deflected land on the paper. By varying the magnitude of the electric field and charge of the drop, you get drops that land at different points on the paper. When this is done thousands of times, you get a printed copy of your work!!! (FYI: This is how older versions of ink-jet printers operate. There is much more to how they operate, but this is the basics!!) Who knows, a passage such as this might be on the MCAT!!!