# CIE AS & A Level Physics : 18.4 Electric field of a point charge – Exam style question – Paper 4

### 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).

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 =  $$\frac{magnitude\, of\, charge\, a}{magnitude\, of\, charge\, b}$$

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, $$E_{A}$$ = $$E_{B}$$

$$Q_{A} / 10^{2}$$ = $$Q_{B} / 52$$

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