Charge Q is uniformly distributed along a thin, flexible rod of length L. The rod is then bent into the semicircle shown in FIGURE. 23.47
a. Find an expression for the electric field at the center of the semicircle.
Hint: A small piece of arc length spans a small angle , where is the radius.
b. Evaluate the field strength if and .
(a) Electrical field at the center of the semicircle is ,
(b) Field strength, when is
The existence of a charged object affects the realm around it, causing an electrical field to create therein space. A charged object produces an electrical field, which could a change within the space or field surrounding it. The extraordinary modification of the realm would be felt by other charges in this field.
radius of the Semicircle,
CALC Charge Q is evenly distributed throughout the length L of a thin, flexible rod. Figure shows how the rod is bent into a semicircle. Graph Cenier
a. Find the following expression for the electric field E at the semicircle's centre: As spans a little angle, a small amount of arc length , where R denotes the radius of the circle. .
and , then
Integrate equations, to
Imposing restrictions to the magnitude of the electrical field,
If and , calculate the field strength.
Given and charge , solve equation
A small object is released at point in the center of the capacitor in FIGURE . For each situation, does the object move to the right, to the left, or remain in place? If it moves, does it accelerate or move at constant speed?
a. A positive object is released from rest.
b. A neutral but polarizable object is released from rest.
c. A negative object is released from rest.
One type of ink-jet printer, called an electrostatic ink-jet printer, forms the letters by using deflecting electrodes to steer charged ink drops up and down vertically as the ink jet sweeps horizontally across the page. The ink jet forms diameter drops of ink, charges them by spraying electrons on the surface, and shoots them toward the page at a speed of . Along the way, the drops pass through two horizontal, parallel electrodes that are wide, and spaced apart. The distance from the center of the electrodes to the paper is . To form the tallest letters, which have a height of , the drops need to be deflected upward (or downward) by . What electric field strength is needed between the electrodes to achieve this deflection? Ink, which consists of dye particles suspended in alcohol, has a density of .
Honeybees acquire a charge while flying due to friction with the air. A bee with a charge of experiences an electric force in the earth’s electric field, which is typically , directed downward.
a. What is the ratio of the electric force on the bee to the bee’s weight?
b. What electric field strength and direction would allow the bee to hang suspended in the air?
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