A metal sphere hangs from a string and has 2 kg of mass the...

Name: a metal sphere hangs from a string and has 2 kg of mass the sphere has a charge of 57 pc a unillorm electric field is turned on and directed to the right a which way does the sphere move lef 65325
Uploaded: 2022-01-25T14:30:03-08:00
Duration: 7 min 38 s
Channel: Vishal Gupta
Description: a metal sphere hangs from a string and has 2 kg of mass the sphere has a charge of 57 pc a unillorm electric field is turned on and directed to the right a which way does the sphere move lef 65325

A metal sphere hangs from a string and has 2 kg of mass. The sphere has a charge of 5.7 pC. A unillorm electric field is turned on and directed to the right. (a) Which way does the sphere move? ◻ left right (b) What is the electric force on the metal sphere if the magnitude of the electric field is 10^(6)(N)/(C) ? ◻ N (c) When the sphere reaches equilibrium, what is the angle that the string makes with the vertical axis (assuming the same electric field as part (b))?

Transcript

00:01 Hi, here in the first part of the given problem, there is a charged sphere which is suspended with the help of a thread in an electric field and under the influence of this electric field.

00:20 This metallic charge is fair, it is making an angle theta with the vertical, where this angle theta is given as 15 .59.

00:35 Degree length of this string length of the thread that is given as 19 .9 centimeter electric field under which it is displaced this electric field is having a magnitude of 1 .00 into 10 raised the part 3 newton per cullum and mass of this sphere metallic sphere that is 2 .00 gram so if we look for all the forces acting on this sphere first of all here this is its weight w which is given as the product of its mass with the acceleration into gravity w is equal to m into g then as it is displaced towards right so electrostatic force acting on it this is q into e and then tension in this thread t so if this angle is theta here this angle that is also vertical it can also be taken as theta so component of the tension in the thread vertical component t cost theta and horizontal component t sine theta now as the sphere is in equilibrium means there should be no net horizontal force acting on it and no net vertical force acting on it means t sine theta that should be equal to q into e and t cos theta that should be equal to m into g so if we divide both of these equations we will get t sine theta by t coss theta is equal to q e by m g canceling this tension here we get 10 theta is equal to q e by m g.

03:30 So finally we get an expression for the charge carried by this sphere and that is m g 10 theta divided by e.

03:42 So here it is for the mass this is 2 grams or 2 into 10 to the power minus 3 kilogram into g which is 9 .8 into 10 of 15 .59 degree and divided by electric field which is 1 .00 into 10 to the power 3.

04:02 So finally this charge here comes out to be equal to 5 .47 into 10 x .6 column or we can say this is q is equal to 5 .47 microlum which is the answer for the first part of this given problem here.

04:26 Now in the second part it is said that electric field is suddenly switched off.

04:35 So as electric field is suddenly switched off...

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