The electric potential in a region of space is , where and are in meters. What are the strength and direction of the electric field at ? Give the direction as an angle or (specify which) from the positive -axis
The strength of the electric field is, pointing degrees below the axis (clockwise).
We have given that the electric potential in a region of space is -, where and are in meters.
We need to find that the strength and direction of the electric field at , ,
Considering the potential
At point , the potential will be
For the electric field, it is a vector quantity. As we have two dimensions, we will have to derive in the two directions; that is
Performing this derivation, we get
For the point , the electric field vector will be
The magnitude of this vector will be
which one could also see as a multiple of right triangle. This is to say that the magnitude of the electric field at the point as.
The direction of the electric field will be
which means that the vector point degrees lower than the direction of the positive axis.
Two metal electrodes are spaced apart and connected by wires to the terminals of a battery.
a. What are the charge on each electrode and the potential difference between them? While the plates are still connected to the battery, insulated handles are used to pull them apart to a new spacing of .
b. What are the charge on each electrode and the potential difference between them?
A nerve cell in its resting state has a membrane potential of , meaning that the potential inside the cell is less than the potential outside due to a layer of negative charge on the inner surface of the cell wall and a layer of positive charge on the outer surface. This effectively makes the cell wall a charged capacitor. When the nerve cell fires, sodium ions,, flood through the cell wall to briefly switch the membrane potential to . Model the central body of a nerve cell-the soma-as a diameter sphere with a -thick cell wall whose dielectric constant is 9.0. Because a cell's diameter is much larger than the wall thickness, it is reasonable to ignore the curvature of the cell and think of it as a parallel-plate capacitor. How many sodium ions enter the cell as it fires?
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