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Chapter 24: Q64P (page 714)

A hollow metal sphere has a potential of +400Vwith respect to ground (defined to be atV=0 ) and a charge of 5.0×10−9C. Find the electric potential at the centre of the sphere.

Short Answer

Expert verified

The electric potential at the centre of the sphere is +400V.

Step by step solution

01

The given data:

Electric potential of hollow sphere with respect to groundV=0,V=+400V

Charge on the sphere, q=5.0×10−9C

02

Understanding the concept of electric potential:

The electric potential of a system is directly proportional to the charge present in the system. Thus, for the given case of the hollow sphere, the charges are all present at the surface of the sphere as it is a conductor. Thus, the electric potential at the surface is equal to the potential at the centre of the sphere.

03

Calculation of the electric potential at the centre of the sphere: 

Since the electric potential throughout the entire conductor is a constant, the electric potential at its center is also+400V.

Hence, the value of the required potential is +400V.

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Most popular questions from this chapter

Question: In Fig. 24-54, how much work must we do to bring a particle, of chargeQ=+16eand initially at rest, along the dashed line from infinity to the indicated point near two fixed particles of chargesq1=+4Eandq2=-q1/2? Distance,d=1.40cm,θ1=43°andθ2=60°

In Fig. 24-66, point P is at distanced1=4.00m from particle 1(q1−2e) and distanced2=2.00m from particle 2 (q2+2e), with both particles fixedin place.

(a) With V=0at infinity, what is V at P? If we bring a particle ofchargeq3+2e from infinity to P,

(b) how much work do we do and

(c) what is the potential energy of the three-particle system?

A spherical drop of water carrying a charge of 30 pChas a potential of 500 Vat its surface (with V = 0at infinity). (a) What is the radius of the drop? (b) If two such drops of the same charge and radius combine to form a single spherical drop, what is the potential at the surface of the new drop?

A long, solid, conducting cylinder has a radius of 2.0 cm. The electric field at the surface of the cylinder is160N/C, directed radially outward. Let A, B, and Cbe points that are10cm, 2.0 cm, and5.0 cm, respectively, from the central axis of the cylinder. What are (a) the magnitude of the electric field at Cand the electric potential differences (b)VB-VCand (c)VA-VB?

In the situation of Question 7, is the work done by your force positive, negative, or zero if the particle is moved (a) from Ato B, (b) from Ato C, and (c) from Bto D? (d) Rank those moves according to the magnitude of the work done by your force, greatest first.
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