Two 3.0 g spheres on 1.0 m-long threads repel each other after being equally charged, as shown…
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Question “Two 3.0 g spheres on 1.0 m-long threads repel each other after being equally charged, as shown…”
Two 3.0 g spheres on 1.0 m-long threads repel each other after being equally charged, as shown in the figure.
What is the charge q?
http://farm5.static.flickr.com/4050/4296660084_be175edea1_o.jpg
Answer
![](https://drive.google.com/uc?id=1V5b8xO-gj7pzCbTKCDGe92CvLfLqOR_K&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
VISUALIZE
The figure above shows the free-body diagram for each point charge q.
T be the tension in each string. F represents the Coulombic force acting between two charges.
Components of force that act on the charge qare
![](https://drive.google.com/uc?id=1q7wPUVudftYiyr3ugqopivgsyyCSu9bt&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=18J6LpTNfBpTTSYBLYut_AMcrXolG9PHH&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
………………….. (1)
![](https://drive.google.com/uc?id=1ZqD7bxK4_B4tj0o6pipjJ9YWXvDA8jqf&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1jqzdGYOl0UnBPMcq_sXz0NspYcfoJv2f&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
…………………. (2)
KNOWN
![](https://drive.google.com/uc?id=1j5u8kMuQSpfLBsndKwq8U60O7kDQMTSZ&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1fGBHvYtwbm2t9t7hNivg5ApAmD6aRpfZ&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1YXLwiRiPbwHA7xiX0dgQrVyjy0bDwwcy&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
Length of each string Media_tag_8$
Acceleration caused by gravity is
![](https://drive.google.com/uc?id=1ytFRGUjDjEfx7zM74i8XlT4iOzQclTGX&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
FIND
We have to determine the value of the charge
![](https://drive.google.com/uc?id=1AFtC5TIic1EjJp_48TWwiB7cou8PGfZK&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
of each point charge.
SOLVED
The above figure shows:
![](https://drive.google.com/uc?id=1FW_32bcbXWkE-xIyGV8cgsT6yD_yyYLK&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1wFZT1IUsxPIIgzGNgHJ5bam_rm9aAtT9&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=14g4iR3WCNMxpqU8_FJL1f-48BYmxU0dN&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1x_52jJAjrzVkoSnQFNObRH0TBnExdXJL&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
charge is therefore seperated.
![](https://drive.google.com/uc?id=1HSpIB57Mw4yiJzXqlDxTnKZVGetFfMtx&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
q is the point charge.
According to the Coulombic force between the point charges, is
![](https://drive.google.com/uc?id=1ap3LAyt5I4BlJhyKau_WFzRQ9NwslLT2&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1Atn_fyzcQJRwqzxZsJdkD7M5F8BFQJdu&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
………………. (3)
Divide the equations (1) and(2) to get
![](https://drive.google.com/uc?id=1oMGNRFTm-PAkh_oeN9F2MuzgESQfn0Cx&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1szOecVHHGZuCUOIbfIMrEvGdt91hv5jP&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1ZCPSdRp6bz3QmzAyRyxoY4knRHb4zX1m&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=176OHSwAZK6kG5lh53RN6yh0KHuXJU7dn&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1kKovffHd9oVcIJ0IBo571QRqFzDChr3I&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1ESXTk_v9VoXnRfrohnuIEcRJira-jwIu&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=17JUbtiNnOd6kAXhvhr0bxtMbDOyWmSCV&export=download/Two-3.0-g-spheres-on-1.0-m-long-threads-repel-each-other-after-being-equally-charged,-as-shown.png?x-oss-process=image/resize,w_560/format,webp)
Conclusion
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