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CAIE A-Level Physics A2 18.5 Electric Potential Questions

Practise calculating electric potential and potential energy for point charges, using potential gradients for field strength and relating signs to work and energy.

Syllabus
2028–2030
Course
Physics 9702
Level
A2

Exam points

  • define and calculate electric potential and point-charge potential, including sign and reference
  • use potential gradient to determine electric field strength and direction
  • calculate electric potential energy of two point charges and relate it to work and energy changes

Covered syllabus points

18.5.1—Electric potential at a point as the work done per unit positive charge in18.5.2—The fact that the electric field at a point is equal to the negative of18.5.3—V = Q / (4πε0 r) for the electric potential in the field due to a point18.5.4—The concept of electric potential leads to the electric potential energy of

Question 1

[Maximum number: 7]

Question (a)

(a)

Define electric potential at a point.

[ 2 ]

Question (b)

(b)

Two isolated charged metal spheres X and Y are near to each other in a vacuum. The centres of the spheres are 1.2 m apart, as shown in Fig. 5.1.

Fig. 5.1 (not to scale)

Fig. 5.1 (not to scale)

Point P is on the line joining the centres of spheres X and Y and is at a variable distance x from the centre of X .

Fig. 5.2 shows the variation with x of the total electric potential V due to the two spheres.

Fig. 5.2

Fig. 5.2

Figure for Question (b) — CAIE A-Level Physics A2

State three conclusions that may be drawn about the spheres from Fig. 5.2. The conclusions may be qualitative or quantitative.

1
2
3

[ 3 ]

Question (c)

(c)

A proton is held at rest on the line joining the centres of the spheres in (b) at the position where x=0.60 mx=0.60 \mathrm{~m}.

The proton is released.
Describe and explain, without calculation, the subsequent motion of the proton.

[ 2 ]

Question 2

[Maximum number: 2]

The electric potential gradient is related to the electric field.

Use data from Fig. 4.2 to state the value of x at which the magnitude of the electric potential gradient is maximum. Give a reason for the value you have chosen.

Question 3

[Maximum number: 7]

Question (a)

(a)

Define electric potential at a point.

[ 2 ]

Question (b)

(b)

An isolated conducting sphere is charged. Fig. 5.1 shows the variation of the potential V due to the sphere with displacement x from its centre.

Fig. 5.1

Fig. 5.1

Use Fig. 5.1 to determine:

[ 3 ]

Question (i)

(i)

the radius of the sphere
radius = m

[ 1 ]

Question (ii)

(ii)

the charge on the sphere.
charge = C

[ 2 ]

Question (c)

(c)

Two spheres are identical to the sphere in (b). Each sphere has the same charge as the sphere in (b).

The spheres are held in a vacuum so that their centres are separated by a distance of 0.46 m . Assume that the charge on each sphere is a point charge at the centre of the sphere.

[ 2 ]

Question (i)

(i)

Calculate the electric potential energy EPE_{\mathrm{P}} of the two spheres.

EP=E_{P}=
[ 2 ]

Question 4

[Maximum number: 2]

Define electric potential at a point.

Question 5

[Maximum number: 1]

A charged sphere X is supported on an insulating stand. A second charged sphere Y is suspended by an insulating thread so that sphere Y is in equilibrium at the position shown in Fig. 4.1.

Fig. 4.1

Fig. 4.1

The charge on sphere X is +96 nC and the charge on sphere Y is +64 nC .
Assume that the spheres behave as point charges.
The length of the thread is 1.2 m and the centres of sphere X and sphere Y are separated horizontally by a distance of 0.080 m .

Calculate the total electric potential energy stored between X and Y .
energy = J

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