Bald patch on cats back

[bobdylannumber1]

I've just noticed a bald patch on my cats back totally bald I only noticed now because she's not a very friendly cat and only sits on my knee if she's been outside Nd is wet r cold she heads off all day might pop back in the afternoon then head off till night time is this mange I wonder

I took her to the vet and he said she may have got a cut and the n picked it gave her injection antibiotic and a collar for a week she's going mad with that on Nd is to stay in she loves going out spends all day outside and then comes in at night but well persevere