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Chapter 24: Q93P (page 716)

A uniform charge of 16.0渭Cis on a thin circular ring lying in xy plane and centered on the origin. The ring鈥檚 radius is3.00cm. If point A is at the origin and point B is on the z-axis at z=4.00cm, what isVB-VA?

Short Answer

Expert verified

The value of VB-VAis -1.92MV.

Step by step solution

01

Step 1: Given data:

The uniform charge,q=+16.0渭C,

The radius of the circle,R=0.03m

The vertical distance, AB=Z=0.04 m.

02

Determining the concept:

Potential at a point due to a charge q is given as,

V=14蟺蔚0qr

Here, is the distance of the point from the charge,q is the electric charge, and14蟺蔚0is the Coulomb constanthaving a value 9脳10N.m2/C2.

03

Determining the VB-VA:

Due to the ring, the electric potential atAis,

VA=14蟺蔚o路qR

=9.0脳109N.m2/C2脳16.0脳10-6C0.03m

=4800脳103V

=4.8 MV

Again, due to the ring, the electric potential at Bis,

VB=14蟺蔚o路qR2+Z2
VB=9.0脳109N.m2/C2脳16脳10-6C0.032+0.042m

=9.0脳109N.m2/C2脳16脳10-6C0.05 m

=2,880脳103V=2.88MV

Now,

VB-VA=2.88MV-4.8MV=-1.92MV

.

Hence, potential at VB-VAis -1.92MV.

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