**Question**

**Question**

(a) State one similarity and one difference between the fields of force produced by an isolated

point charge and by an isolated point mass.

similarity:

difference:

(b) An isolated solid metal sphere A of radius R has charge +Q, as illustrated in Fig. 5.1.

A point P is distance 2R from the surface of the sphere.

Determine an expression that includes the terms R and Q for the electric field strength E at

point P.

E = …………………………………………………

(c) A second identical solid metal sphere B is now placed near sphere A. The centres of the

spheres are separated by a distance 6R, as shown in Fig. 5.2.

Point P lies midway between spheres A and B.

Sphere B has charge –Q.

Explain why:

(i) the magnitude of the electric field strength at P is given by the sum of the magnitudes of

the field strengths due to each sphere

(ii) the electric field strength at point P due to the charged metal spheres is not, in practice,

equal to 2E, where E is the electric field strength determined in (b).

**Answer/Explanation**

**Answer:**

(a) similarity: both are radial

or

both have inverse square (variations)

difference: direction is always/only towards the mass

or

direction can be towards or away from charge

(b) field strength = \(Q / 4 π ε_0x^2\)

\(E = Q / 36 π ε_0R^2\)

(c) (i) fields (due to each sphere) are in same direction

(ii) charges on spheres attract/affect each other

or

charge distribution on each sphere distorted by the other sphere

or

charges on the surface of the spheres move

*Question*

(a) State what is meant by *electric field strength*.

(b) Two point charges A and B are situated a distance 15cm apart in a vacuum, as illustrated in Fig. 5.1.

Point P lies on the line joining the charges and is a distance *x* from charge A.

The variation with distance *x* of the electric field strength *E* at point P is shown in Fig. 5.2.

(i) By reference to the direction of the electric field, state and explain whether the charges A and B have the same, or opposite, signs.

(ii) State why, although charge A is a point charge, the electric field strength between *x* = \(3\)cm and *x* = \(7\)cm does not obey an inverse-square law.

(iii) Use Fig. 5.2 to determine the ratio = \(\frac{magnitude\, of\, charge\, a}{magnitude\, of\, charge\, b}\)

**Answer/Explanation**

Ans:

(a) force per unit charge

(force on) positive charge

(b) (i) field changes direction (between A and B)/field is zero at a point (between A and B)

so charges have same sign

(ii) Any one from:

• field is (also) influenced by charge B

• charge A is not isolated/is not the only charge present

• field is due to two/both charges

• field is the resultant of two fields

(iii) *E* = \(Q / (4 \pi ε_{0} x^{2})\)

at *x* = \(10\) cm, \(E_{A}\) = \(E_{B}\)

\(Q_{A} / 10^{2}\) = \(Q_{B} / 52\)